Publications of Eugene B. Dynkin II, Research Papers

Here is a list of research papers arranged chronologically. Parts I and III of the publication list are books and miscellanea (popular articles, book reviews etc).

Abbreviations for the principal Russian mathematical journals:

  • DAN - Doklady Akademii Nauk SSSR,


English translation (published by the American Math. Society) Soviet Mathematics - Doklady.

  • MSb - Mathematicheskii Sbornik,


English translation (published by the American Math. Society) Mathematics of the USSR - Sbornik.

  • IAN - Ivzvestiya Akademii Nauk SSR, Matematicheskaya Seriya,


English translation (published by the American Math. Society) Mathematics of the USSR - Izvestija.

  • UMN - Uspekhi Matematicheskikh Nauk,


English Translation (published by the London Math. Soc. and the British Library) Russian Mathematical Surveys.

  • TV - Teoriya Veroyatnostei i ee Primeneniya,


English Translation (published by the SIAM) Theory of Probability and its Applications.

List of Papers

As a rule we refer to the original Russian publication. Sometimes we mention (in the brackets { }) the volume, issue and pages of the English translation.

  1. On the characteristic roots of a stochastic matrix (with N. A. Dmitriev), DAN 49 (1945), 159-162

 

  1. Classification of the simple Lie groups, MSb 18, 3 (60) (1946), 347 - 353

 

  1. On characteristic roots of stochastic matrices (with N. A. Dmitriev), IAN 10 (1946), 167-184


{Amer. Math. Transl. (2), 140 (1988), 57-77}

  1. An effective construction of Lie groups from Lie algebras, UMN 2,3 (19) (1947), 192

 

  1. The structure of semi-simple Lie algebras, UMN, 2, 4, (20) (1947), 59-127


{Amer. Math. Soc. Transl. (1950),no.17 143 pp}

  1. Calculation of the coefficients in the Campbell- Hausdorff formula, DAN57 (1947), 323-326

 

  1. Normed Lie algebras and analytic groups, UMN3, 3 (25) (1948), 157 - 158

 

  1. On a problem of the probability theory, UMN4, 5 (33) (1949), 183-197

 

  1. On the representation by means of commutators of the series log exey for noncommuting x, y, MSb25 (67) (1949), 155-162

Normed Lie algebras and analytic groups, UMN5, 1 (35) (1950), 135-186


{Amer. Math. Soc. Transl. Series 1, Vol. 9 (1962), 470-542}

  1. On relations of inclusion for irreducible subgroups of the group of matrices, UMN5, 1, (35) (1950), 214

 

  1. Some properties of the system of weights of a linear representation of a semisimple Lie group, DAN71, 2 (1950), 221-224

 

  1. Regular semisimple subsalgebras of semisimple Lie algebras, DAN73, 5 (1950), 877-880

 

  1. Maximal subgroups of semisimple Lie groups and the classification of primitive groups of transformations, DAN75, 3 (1950), 333-336

 

  1. On sufficient and necessary statistics for a family of probability distributions, DAN75, 2 (1950), 161-164

 

  1. Automorphisms of semisimple Lie algebras, DAN76, 5 (1951), 629-632

 

  1. Necessary and sufficient statistics for a family of probabiity distributions, UMN6, 1 (41) (1951), 68-90


{Selected Translations in Math. Statist. and Probab., Vol. 1 (1961), 17-40}

  1. The relations of inclusion between irreducible groups of linear transformations, DAN78, 1 (1951), 5-7

 

  1. On semisimple subalgebras of semisimple Lie algebras, DAN81, 6 (1951), 987-990

 

  1. Maximal subgroups of the classical groups, Trudy Moscov. Mat. Obsh.1 (1952), 39-166


{Amer. Math. Soc. Transl., Series 2, Vol. 6 (1957), 245-378}

  1. Semisimple subalgebras of semisimple Lie algebras, MSb30, (72) (1952), 349-462


{Amer. Math. Soc. Transl., Series 2, Vol. 6 (1957), 111-244}

  1. Topological invariants of linear representations of the unitary group, DAN85, 4 (1952), 697-699

 

  1. Criteria of continuity and of absence of discontinuities of the second kind for trajectories of a Markov stochastic process, IAN16, 6 (1952), 563-572

 

  1. Topological invariants of subgroups of the group of unitary matrices, UMN7, 4 (50)} (1952), 142-143

 

  1. A connection between homologies of a compact Lie group and its subgroups, DAN87, 3 (1952), 333-336

 

  1. Classes of equivalent random variables, UMN8, 2 (54) (1953), 125-130

 

  1. Construction of primitive cycles in compact Lie groups, DAN91, 2 (1953), 201-204

 

  1. On topology of compact Lie groups, UMN8, 3 (55) (1953), 174-175

 

  1. Homologies of compact Lie groups, UMN8, 5 (57) (1953), 73-120


Corrections: UMN 9, 2(60) (1954), 233
{Amer. Math Soc. Transl. Series 2, Vol. 12, 251-300}

  1. Homological characteristics of homomorphisms of compact Lie groups, DAN91, 5 (1953), 1007-1009

 

  1. On some limit theorems for Markov chains, Ukrain. Mat. Zhurnal6, 1 (1954), 21-27

 

  1. Topological characteristics of homomorphisms of compact Lie groups, MSb35 (77), 1 (1954), 129-173


{Amer. Math. Soc. Transl., Series 2, Vol. 12 (1959), 301-342}

  1. Some limit theorems for sums of independent random variables with infinite mathematical expectations, IAN19 (1955), 247-266


{Selected Transl. in Math. Statist. and Probability, Vol. 1 (1961), IMS-AMS, 171-189}

  1. Compact global Lie groups (with A. L. Onishchik), UMN10, 4 (66) (1955), 3-74 {Amer. Math. Soc. Transl., Series 2, Vol. 21 (1962), 119-192}

 

  1. Functionals of trajectories of Markov stochastic processes, DAN104, 5 (1955), 691-694

 

  1. Infinitesimal operators of Markov stochastic processes, DAN105, 2 (1955), 206-209

 

  1. Continuous one-dimensional Markov processes, DAN105, 3 (1955), 405-408

 

  1. On new analytic methods in the theory of Markov stochastic processes, Vestnik Leningrad. Gos. Univ.10(1955), no. 11, 69-74

 

  1. Markov processes and semi-groups of operators, TV1 (1956), 25-37

 

  1. Strong Markov processes (with A. A. Yushkevich), TV1 (1956), 149-155

 

  1. Infinitesimal operators of Markov processes, TV1 (1956), 38-60
  1. Markov processes - continuous parameter, Proceedings of the Third All-Union Congress of Mathematicians (Moscow, 1956), Vol.2, 44-47

 

  1. Inhomogeneous strong Markov processes, DAN113, 2 (1957), 261-263

 

  1. Jump Markov processes, TV3, 1 (1958), 41-60

 

  1. New methods in the theory of Markov processes, Proceedings of the Third All-Union Congress of Mathematicians, Vol. 3, Moscow (1959), 334-342

 

  1. One-dimensional continuous strong Markov processes, TV4, 1 (1959), 3-54

 

  1. Intrinsic topology and excessive functions connected with a Markov process, DAN127 (1959), 17-19


{Selected Transl. in Math. Statistics and Probability, Vol. 3, 327-330}

  1. Linear algebra, In Mathematics in the USSR for 40 years, Vol. 1,207-212; GIFML, Moscow, 1959

 

  1. Lie groups, In Mathematics in the USSR for 40 years Vol. 1, 213-227; GIFML, Moscow 1959

 

  1. Markov processes and related problems of analysis, UMN15, 2 (92) (1960), 3-24,


{Hungarian transl. Magyar Tud. Acad.Mat.Fiz.Oszt.Kozl.17 1967, 231-251}

  1. Markov processes and their subprocesses, Proceedings of All-Union Conference on Probability Theory and Math. Statistics (Erevan, 1958), 223-235; Izdat. Akad. Nauk. Armyan. SSR, Erevan, 1960
  1. On some transformations of Markov processes, DAN133, 2 (1960), 269-272

 

  1. Additive functionals of the Wiener process determined by stochastic integrals, TV5, 4 (1960), 441-452

 

  1. Topologies associated with a Markov process and the strong Markov property (with I. V. Girsanov), TV5, 3 (1960), 375

 

  1. Random walks on groups with a finite number of generators (with M. B. Malyutov), DAN137, 5 (1961), 1042-1045

 

  1. Transformations of Markov processes connected with additive functions, Proc. 4th Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1960), vol. 2, 117-142; University of California Press, Berkeley, Calif.

 

  1. Non-negative eigenfunctions of the Laplace-Beltrami operator and Brownian motion in certain symmetric spaces, DAN141, 2 (1961), 288-292

 

  1. Brownian motion with killing measure mu and speed measure nu, DAN144, 3 (1962), 483-486

 

  1. Markov processes and problems in analysis, Proc. Intern. Congress of Mathematicians (Stockholm, 1962), pp 36-58; Inst. Mittag-Leffler, Djursholm, 1963


{Amer. Math. Soc. Transl., Series 2, Vol. 31, 1-24}

  1. Optimal choice of the stopping time of a Markov process, DAN150, 2 (1963), 238-240

 

  1. Some problems of the theory of differential equations connected with Markov processes, Outlines Joint Soviet-American Sympos. Partial Differential Equations (Novosibirsk, 1963), 67-72; Academ. Sci. USSR, Siberian Branch, Moscow 1963

 

  1. Non-negative solutions of a boundary value problem with oblique derivative, DAN157, 5 (1964), 1028-1030

 

  1. Martin boundary and non-negative solutions of a boundary value problem with oblique derivative, UMN19, 5 (119) (1964), 3-50,


Letter to the Editor 19, 6 (120), 255-256

  1. Martin boundaries, Winter School of Theory of Probability and Math. Statistics (Uzhgorod, 1964), 87-124; Izdat. Akad. Nauk Ukrain. SSR, Kiev, 1964

 

  1. Controlled random sequences, TV10, 1 (1965), 3-18

 

  1. Martin boundary and positive solutions of some boundary value problems, Annales de l'Institut Fourier (Grenoble)15, 1 (1965), 275-282
  1. Brownian motion in certain symmetric spaces and non-negative eigenfunctions of the Laplace-Beltrami operator, IAN30, 2 (1966), 455-478


{Amer. Math. Soc. Transl., Series 2, 72 (1968), 203-228}

  1. General boundary conditions for Markov processes with denumerable set of states, International Congress of Mathematicians (Moscow, 1966), Abstracts of Short Communications, Section 11, 35-36

 

  1. General additional conditions for a boundary value problem with oblique derivative, DAN168, 4 (1966), 737-739

 

  1. General boundary conditions for denumerable Markov processes, DAN172, 2 (1967), 258-261

 

  1. General boundary conditions for denumerable Markov processes, TV12, 2 (1967), 222-257;


Letter to the Editor 13, 2 (1967), 379

  1. General lateral conditions for some diffusion processes, Proc. 5th Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66; Vol.2, Part 2, 17-49; Univ. of California Press, Berkeley, Calif. 1967

 

  1. Diffusion of tensors, DAN179, 6 (1968), 1264-1267


{9,2, 532-535}

  1. Sufficient statistics for the optimal stopping problem, TV13, 1 (1968), 150-152


Letter to the Editor TV13, 4 (1968), 755

  1. On the origins of the wanderings of Markov processes (with A. A. Yushkevich), TV13, 3 (1968), 490-493

 

  1. On extensions of a Markov process TV13, 4 (1968), 708-713

 

  1. Martin boundaries, The Fourth Summer School (Katsiveli, 1966), 5-41, Naukova Dumka, Kiev 1968

 

  1. A game version of an optimal stopping problem, DAN185, 1 (1969), 16-19


{10,2, 270-274}

  1. Boundary theory for Markov processes (discrete case), UMN24, 2 (146) (1969), 3-42


{24, 2, 1-42}

  1. Exit space of a Markov process, UMN24, 4 (148) (1969), 89-152 {24, 4, 89-157}

 

  1. Excessive functions and the exit-space of a Markov process, TV15, 1 (1970), 38-55

 

  1. Classes of similar Markov processes and corresponding exit and entrance spaces, J. Sci., Univ. Tokyo, Sec. 117, 1-2 (1970), 87-100

 

  1. Excessive measures and entrance laws for a Markov process, MSb84, 2 (126) (1971), 218-253


{13, 2, 209-246}

  1. Initial and final behaviour of the trajectories of Markov processes, UMN26, 4 (160) (1971), 153-172


{26, 4 165-185}

  1. Wanderings of a Markov process, TV16, 3 (1971), 409-436


{16, 401-428}

  1. Entrance and exit spaces for a Markov Process, Actes du Congr�s International des Math�maticiens (Nice, 1970), Tome 2, 507-512; Gauthier-Villars, Paris, 1971

 

  1. Supermartingales with random birth times, UMN26, 6 (162), 1971, 241-242

 

  1. Some probability models for an expanding economy, DAN200 (1971), 523-525


{ 12 , 5, 1422-1425}

  1. Optimal control for a sequence of sums of independent random variables, Ekonom. i Mat. Metody7, 6 (1971), 901-903

 

  1. Integral representation of excessive measures and excessive functions, UMN27, 1 (163) (1972), 43-80


{ 27, 1, 43-84}

  1. Stochastic concave dynamic programming, MSb87 (129), 4 (1972), 490-503


{16, 4, 501-515}

  1. Regular Markov processes, UMN28, 2 (170) (1973), 35-64


{28, 2, 33-64}

  1. Duality in the theory of Markov process, International Conference on Probability Theory and Mathematical Statistics (Vilnius, 1973), Abstracts of Communications, Vol. 1, 213-216

 

  1. Optimal programs and stimulating prices in the stochastic models of economic growth, Math. Models in Economics ( Proc. Sympos. and Conf. on von Neumann Models, Warsaw, 1972) J. \Lo\'s and M. W. \Lo\'s, eds, pp. 207-218; North-Holland, Amsterdam; Elsevier, New York; PWN, Warszawa, 1974

 

  1. Determining functions of Markov processes and corresponding dual regular classes (with S. E. Kuznetsov), DAN214, 1 (1974), 25-28


{15, 1 20-23}

  1. Additive functionals of Markov processes and their spectral measures, DAN214, 6 (1974), 1241-1244


{15, 1, 330-334}

  1. Markov representations of stochastic systems, DAN218 (1974), 1009-1012


{15, 5 1442-1446}

  1. Markov representations of stochastic systems UMN30, 1, (181) (1975), 61-99


{30, 1 64-104}

  1. Stochastic dynamical models of economic equilibrium, Proc. of the International Congress of Mathematicians (Vancouver, BC, 1974), Vol. 2, 509-515; Canad. Math. Congress, Montreal Que, 1975

 

  1. On preference relations under uncertainty (with A. I. Ovseevich), Ekonomika i Mat. Metody 11, 2 (1975), 393-395

 

  1. Additive functionals of Markov processes and stochastic systems, Collection of articles dedicated to Marcel Brelot on the occasion of his 70th birthday, Ann. Inst. Fourier (Grenoble)25, 3-4 (1975), 177-200


Correction: 26 (1976), no.1, 1 loose p.

  1. Regular conditional mathematical expectations of correspondences (with I. V. Evstingneev), TV21, 2 (1976), 334-347

 

  1. Economic equilibrium under uncertainity, Computing Equilibria, How and Why (Proc. Internat. Conf. Comput. Centre, Polish Acad. Sci. Torun, 1974), J. \Lo's and M. W. \Lo's, eds, pp. 41-60; PWN (1976); Warszawa; North-Holland, Amsterdam, 1976.

 

  1. On a new approach to Markov processes, Proceedings of the Third Japan-USSR Symposium on Probability Theory (Tashkent, 1975), pp. 42-64. Lecture Notes in Math., vol. 550, Springer, Berlin 1976.

 

  1. Markov systems and their additive functionals, Annals of Probability5 (1977), 653-677

 

  1. Sufficient statistics and extreme points, Ann. Probab. 6 (1978), 705-730.


{Chinese transl.Yingyong Shuxue yu Jisuan Shuxue 1980, no. 6, 48-65}

  1. On duality for Markov processes, Stochastic analysis (Proc. Internat. Conf. Northwestern Univ., Evanston, Ill, 1978) , A. Friedman and M. Pinsky, eds, pp. 63-77; Academic Press, New York-London, 1978.

 

  1. Minimal excessive measures and functions, Trans. Amer. Math. Soc.258 (1980), 217-244

 

  1. Markov processes and random fields, Bull. Amer. Math. Soc. (N. S.)3, (1980) no.3, 975-999

 

  1. Markov processes, random fields and Dirichlet spaces, Physics Report77, 3 (1980), 239-247

 

  1. Additive functionals of several time-reversible Markov processes, J. Funct. Anal.42, (1980), no. 1, 64-101

 

  1. Harmonic functions associated with several Markov processes, Adv. in Appl. Math.2 (1981), 260-283

 

  1. Green's and Dirichlet spaces associated with fine Markov processes, J. Funct. Anal.47 (1982), no.3, 381-418

 

  1. Green's and Dirichlet spaces for a symmetric Markov transition functions, Probability, Statistics and Analysis, J. F. C. Kingman and G. E. H. Reuter, eds; pp. 79-98;, London Math. Soc. Lecture Note Ser. 79; Cambridge University Press, Cambridge-New York, 1983.

 

  1. Stochastic waves (with R. J. Vanderbei), Trans. Amer. Math. Soc.275 (1983),no.2 771-779

 

  1. Markov processes as a tool in field theory, J. Funct. Anal.50, (1983), no.2, 167-187

 

  1. Gaussian random fields and Gaussian evolutions, Theory and Applications of Random fields (Bangalore, 1982), G. Kallianpur, ed.,pp. 28-39; Lecture Notes in Control and Information Sci. 49, Springer, Berlin-New York, 1983.

 

  1. Symmetric statistics, Poisson point processes and multiple Wiener integrals (with A. Mandelbaum), Ann. Statist.11, (1983),no.3 739-745

 

  1. Gaussian and non-Gaussian random fields associated with Markov processes, J. Funct. Anal.55 (1984), no. 3, 344-376

 

  1. Polynomials of the occupation field and related random fields, J. Funct. Anal.58 (1984), no.1 20-52

 

  1. Local times and quantum fields Seminar on Stochastic Processes (Gainsville, Fla.) E. Cinlar, K. L. Chung, R. K. Getoor, eds, pp. 69-83, Birkh�user, Boston, 1984.

 

  1. An application of flows to time shift and time reversal in stochastic processes, Trans. Amer. Math. Soc.287 (1985), no.2, 613-619

 

  1. Random fields associated with multiple points of the Brownian motion, J. Funct. Anal.62 (1985), no.3, 397-434

 

  1. Additive functionals and entrance laws (with R. K. Getoor), J. Funct. Anal.62 (1985), 221-265

 

  1. Multiple path integals, Adv. in Appl. Math.7 (1986), no. 2, 205-219

 

  1. Generalized random fields related to self-intersections of the Brownian motion, Proc. Nat. Acad. Sci. USA83 (1986), no.11 3573-3576

 

  1. Functionals associated with self-intersections of the planar Brownian motion, S�minaire de Probabilit�s, XX, 1984/85, pp. 553-571, J. Az�ma, M. Yor, eds; Lecture Notes in Math., 1204, Springer, Berlin/New York, 1986.

 

  1. Self-intersection local times, occupation fields and stochastic integrals, Adv. in Math.65 (1987), no. 3, 254-271.

 

  1. Stochastic processes on random domains (with P. J. Fitzsimmons), Ann. Inst. H. Poincar� Probab. Statist. 23 (1987),no. 2, suppl. 379-396.

 

  1. Regularized self-intersection local times of planar Brownian motion, Ann. Probab.16 (1988), no. 1, 58-74
  1. Self-intersection gauge for random walks and for Brownian motion, Ann. Probab.16 (1988), no. 1, 1-57

 

  1. Representation for functionals of superprocesses by multiple stochastic integrals, with applications to self-intersectional local times, Colloque Paul L�vy sur le Processus Stochastiques (Palaiseau, 1987). Ast�risque157-158 (1988), 147-171

 

  1. Superprocesses and their linear additive functionals, Trans. Amer. Math. Soc.314 (1989), 255-282

 

  1. Three classes of infinite dimensional diffusions, J. Funct. Anal.86 (1989), no.1 75-110

 

  1. Kolmogorov and theory of Markov processes Ann. Probab.17 (1989), no. 3, 822-832

 

  1. Regular transition functions and regular superprocesses, Trans. Amer. Math. Soc.316 (1989), no.2, 623-634

 

  1. Branching particle systems and superprocesses, Ann. Probab.19, 3 (1991), 1157-1194

 

  1. A probabilistic approach to one class of nonlinear differential equations, Probab. Theory Rel. Fields 89 (1991), 89-115

 

  1. Path processes and historical superprocesses, Probab. Theory Rel. Fields 90 (1991), no. 1, 1-36

 

  1. Additive functionals of superdiffusion processes, Random Walks, Brownian Motion and Interacting Particle Systems, pp.269-281; R. Durrett, H. Kesten, eds; Progr. Probab, 28; Birkh�user, Boston, 1991.

 

  1. Superdiffusions and parabolic nonlinear differential equations Ann. Probab.20 (1992), no.2, 942-962

 

  1. Birth delay of a Markov process and the stopping distributions for regular processes, Probab. Theory Rel. Fields 94 (1993), no. 3, 399-411.

 

  1. On regularity of superprocesses, Probab. Theory Rel. Fields 95 (1993), no.2, 263-281

 

  1. Superprocesses and partial differential equations (The 1991 Wald Memorial Lecture), Ann. Probab.21 (1993), no. 3, 1185-1262

 

  1. Branching measure-valued processes (with S. E. Kuznetsov and A. V. Skorokhod), Probab. Theory Rel. Fields99 (1994), 55-96

 

  1. A type of interaction between superprocesses and branching particle systems, Measure-valued Processes, Stochastic Partial Differential Equations and Interacting systems (Montreal 1992) , pp.83-86; CRM Monograph Series, vol. 5, ed. D. A. Dawson , Amer. Math. Soc., Providence, R.I., 1994

 

  1. Branching with a single point catalyst, Stochastic Analysis (Ithaca, N.Y., 1993), Proc. Sympos. Pure Math. 57, 423-425; Amer. Math. Soc., Providence, R.I., 1995

 

  1. Markov snakes and superprocesses (with S. E. Kuznetsov), Probab. Theor. Rel. Fields , 103 (1995), no.4, 433-473

 

  1. Superdiffusions and removable singularities for quasilinear partial differential equations (with S. E. Kuznetsov), Comm. Pure Appl.Math.49 (1996), 125-176

 

  1. Solutions of Lu =ua dominated by L-harmonic functions (with S.E. Kuznetsov), J. Anal. Math., 68 (1996), 15-37

 

  1. Linear additive functionals of superdiffusions and related nonlinear P.D.E. (with S.E. Kuznetsov), Trans. Amer. Math. Soc.348 (1996), 1959-1987

 

  1. L�vy measure of superprocesses; absorption process, Ito's Stochastic Calculus and Probability Theory , eds. N.Ikeda, S.Watanabe, M. Fukushima, H. Kunita, pp. 1-14, Springer Berlin/New York, 1996

 

  1. Natural linear additive functionals of superprocesses (with S.E. Kuznetsov), Ann. Probab., 25 (1997), no. 2, 640-661

 

  1. Nonlinear parabolic P.D.E. and additive functionals of superdiffusions (with S.E. Kuznetsov), Annals Probab., 25 (1997), no. 2, 662-701

 

  1. A probabilistic approach to a nonlinear differential equation on a Riemannian manifold, TV, 42 (1997), 336-341

 

  1. Polylinear additive functionals of superprocesses, J. Functional Analysis, 148 (1997), 148-257

 

  1. A new relation between diffusions and superdiffusions with applications to the equation Lu =ua, C.R. Acad. Sci. Paris, S�rie I, 35 (1997), 439-444

 

  1. Trace on the boundary for solutions of nonlinear differential equations (with S.E. Kuznetsov), Transactions of Americ. Math. Soc. , 350 (1998), no. 11, 4499-4519

 

  1. Solutions of nonlinear differential equations on a Riemannian manifold and their trace on the Martin boundary (with S.E.Kuznetsov), Trans. Americ. Math. Soc. , 350 (1998), no. 11, 4521-4552

 

  1. Stochastic boundary values and boundary singularities for solutions of the equation Lu =ua. J. Functional Analysis, 153 (1998), 147-186

 

  1. Fine topology and fine trace on the boundary associated with a class of semilinear differential equations (with S. E. Kuznetsov), Comm. Pure Appl.Math., 51 (1998), 897-936

 

  1. Semilinear parabolic equations, diffusions and superdiffusions, J. Functional Analysis, 158 (1998), 325-356

 

  1. Extinction of superdiffusions and semilinear PDEs (with S. E. Kuznetsov), J. Functional Analysis 162(1999), 346-378

 

  1. Solutions of a class of semilinear differential equations: trace and singularities on the boundary (with S. E. Kuznetsov), Operator Theory:Advances and Applications110(1999), 69-80

 

  1. Exit laws and excessive functions for superprocesses, TV44 (1999), 880-885

 

  1. Probability and nonlinear analysis, Canadian Mathematical Society Conference Proceedings, 28 (2000), 139-144

 

  1. Solutions of semilinear equations related to harmonic functions, J. Functional Analysis 170 (2000),464-474

 

  1. A probabilistic approach to the equation Lu =-u2, J. Functional Analysis 170 (2000),450-463

 

  1. Rough boundary trace for solutions of Lu=\psi(u) (with S.E.Kuznetsov), TV45 (2000),740-744

 

  1. Branching exit Markov systems and superprocesses, Annals Probab. 29 (2001), 1833-1858
  1. Poisson capacities, Mathematical Research  Letters, 10 (2003), 85-95
  1. Harmonic functions and exit boundary of superdiffusion, J. Functional Analysis, 206  (2004),   31-68     
  1. Branching exit Markov systems and their applications to partial differential equations, In Markov Processes and Controlled Markov Chains, Zhenting Hou, Jerzy A. P. Filar and Anyue Chen (Eds.), 3-13, Kluver Academic Publishers, Dordrecht/ Boston/ London, 2002
  1. On upper bounds for positive solutions of semilinear equations,  J. Functional Analysis, 210 (2004), 73-100
  1. N-measures for branching exit Markov systems and their applications to differential equations (with S.E.Kuznetsov), Probab. Theory Relat. Fields,  130 (2004), 135-150
  1. A new inequality for superdiffusions and its applications to nonlinear differential equations, Electronic Research Announcements, AMS, 10 (August 2, 2004), 68-77
  1. Absolute comtinuity results for superdiffusions with applications to differential equations,  C.R. Acad. Sci. Paris, Ser. I, 338 (2004), 605-610
  1. Superdiffusions and positive solutions of nonlinear partial differential equations,  UMN, 59:1(355) (2004), 145-156 (in Russian);: Russian Mathematical Surveys 59:1 (2004), 147-156 (in English)
  1. On extreme X-harmonic functions, Mathematical Research Letters, 13 (2006), no. 1, 59-69
  1. A note on X-harmonic functions, Illinois J. Math., 50:2 (2006), 385-394
  1. An application of probability to nonlinear analysis, In: Stochastic Analysis and Applications, The Abel Symposium 2005, Springer, 2007, 309-325  
  1. Bessel capacities on compact manifolds and their relation to Poisson capacities, J. Functional Analysis, 242 (2007), 281-294

A class of boundary traces for solutions of the equation Lu=\psi(u),  J. Functional Analysis,   Publications of Eugene B. Dynkin II, Research Papers

Here is a list of research papers arranged chronologically. Parts I and III of the publication list are books and miscellanea (popular articles, book reviews etc).

Abbreviations for the principal Russian mathematical journals:

  • DAN - Doklady Akademii Nauk SSSR,


English translation (published by the American Math. Society) Soviet Mathematics - Doklady.

  • MSb - Mathematicheskii Sbornik,


English translation (published by the American Math. Society) Mathematics of the USSR - Sbornik.

  • IAN - Ivzvestiya Akademii Nauk SSR, Matematicheskaya Seriya,


English translation (published by the American Math. Society) Mathematics of the USSR - Izvestija.

  • UMN - Uspekhi Matematicheskikh Nauk,


English Translation (published by the London Math. Soc. and the British Library) Russian Mathematical Surveys.

  • TV - Teoriya Veroyatnostei i ee Primeneniya,


English Translation (published by the SIAM) Theory of Probability and its Applications.

List of Papers

As a rule we refer to the original Russian publication. Sometimes we mention (in the brackets { }) the volume, issue and pages of the English translation.

  1. On the characteristic roots of a stochastic matrix (with N. A. Dmitriev), DAN 49 (1945), 159-162

 

  1. Classification of the simple Lie groups, MSb 18, 3 (60) (1946), 347 - 353

 

  1. On characteristic roots of stochastic matrices (with N. A. Dmitriev), IAN 10 (1946), 167-184


{Amer. Math. Transl. (2), 140 (1988), 57-77}

  1. An effective construction of Lie groups from Lie algebras, UMN 2,3 (19) (1947), 192

 

  1. The structure of semi-simple Lie algebras, UMN, 2, 4, (20) (1947), 59-127


{Amer. Math. Soc. Transl. (1950),no.17 143 pp}

  1. Calculation of the coefficients in the Campbell- Hausdorff formula, DAN57 (1947), 323-326

 

  1. Normed Lie algebras and analytic groups, UMN3, 3 (25) (1948), 157 - 158

 

  1. On a problem of the probability theory, UMN4, 5 (33) (1949), 183-197

 

  1. On the representation by means of commutators of the series log exey for noncommuting x, y, MSb25 (67) (1949), 155-162

Normed Lie algebras and analytic groups, UMN5, 1 (35) (1950), 135-186


{Amer. Math. Soc. Transl. Series 1, Vol. 9 (1962), 470-542}

  1. On relations of inclusion for irreducible subgroups of the group of matrices, UMN5, 1, (35) (1950), 214

 

  1. Some properties of the system of weights of a linear representation of a semisimple Lie group, DAN71, 2 (1950), 221-224

 

  1. Regular semisimple subsalgebras of semisimple Lie algebras, DAN73, 5 (1950), 877-880

 

  1. Maximal subgroups of semisimple Lie groups and the classification of primitive groups of transformations, DAN75, 3 (1950), 333-336

 

  1. On sufficient and necessary statistics for a family of probability distributions, DAN75, 2 (1950), 161-164

 

  1. Automorphisms of semisimple Lie algebras, DAN76, 5 (1951), 629-632

 

  1. Necessary and sufficient statistics for a family of probabiity distributions, UMN6, 1 (41) (1951), 68-90


{Selected Translations in Math. Statist. and Probab., Vol. 1 (1961), 17-40}

  1. The relations of inclusion between irreducible groups of linear transformations, DAN78, 1 (1951), 5-7

 

  1. On semisimple subalgebras of semisimple Lie algebras, DAN81, 6 (1951), 987-990

 

  1. Maximal subgroups of the classical groups, Trudy Moscov. Mat. Obsh.1 (1952), 39-166


{Amer. Math. Soc. Transl., Series 2, Vol. 6 (1957), 245-378}

  1. Semisimple subalgebras of semisimple Lie algebras, MSb30, (72) (1952), 349-462


{Amer. Math. Soc. Transl., Series 2, Vol. 6 (1957), 111-244}

  1. Topological invariants of linear representations of the unitary group, DAN85, 4 (1952), 697-699

 

  1. Criteria of continuity and of absence of discontinuities of the second kind for trajectories of a Markov stochastic process, IAN16, 6 (1952), 563-572

 

  1. Topological invariants of subgroups of the group of unitary matrices, UMN7, 4 (50)} (1952), 142-143

 

  1. A connection between homologies of a compact Lie group and its subgroups, DAN87, 3 (1952), 333-336

 

  1. Classes of equivalent random variables, UMN8, 2 (54) (1953), 125-130

 

  1. Construction of primitive cycles in compact Lie groups, DAN91, 2 (1953), 201-204

 

  1. On topology of compact Lie groups, UMN8, 3 (55) (1953), 174-175

 

  1. Homologies of compact Lie groups, UMN8, 5 (57) (1953), 73-120


Corrections: UMN 9, 2(60) (1954), 233
{Amer. Math Soc. Transl. Series 2, Vol. 12, 251-300}

  1. Homological characteristics of homomorphisms of compact Lie groups, DAN91, 5 (1953), 1007-1009

 

  1. On some limit theorems for Markov chains, Ukrain. Mat. Zhurnal6, 1 (1954), 21-27

 

  1. Topological characteristics of homomorphisms of compact Lie groups, MSb35 (77), 1 (1954), 129-173


{Amer. Math. Soc. Transl., Series 2, Vol. 12 (1959), 301-342}

  1. Some limit theorems for sums of independent random variables with infinite mathematical expectations, IAN19 (1955), 247-266


{Selected Transl. in Math. Statist. and Probability, Vol. 1 (1961), IMS-AMS, 171-189}

  1. Compact global Lie groups (with A. L. Onishchik), UMN10, 4 (66) (1955), 3-74 {Amer. Math. Soc. Transl., Series 2, Vol. 21 (1962), 119-192}

 

  1. Functionals of trajectories of Markov stochastic processes, DAN104, 5 (1955), 691-694

 

  1. Infinitesimal operators of Markov stochastic processes, DAN105, 2 (1955), 206-209

 

  1. Continuous one-dimensional Markov processes, DAN105, 3 (1955), 405-408

 

  1. On new analytic methods in the theory of Markov stochastic processes, Vestnik Leningrad. Gos. Univ.10(1955), no. 11, 69-74

 

  1. Markov processes and semi-groups of operators, TV1 (1956), 25-37

 

  1. Strong Markov processes (with A. A. Yushkevich), TV1 (1956), 149-155

 

  1. Infinitesimal operators of Markov processes, TV1 (1956), 38-60
  1. Markov processes - continuous parameter, Proceedings of the Third All-Union Congress of Mathematicians (Moscow, 1956), Vol.2, 44-47

 

  1. Inhomogeneous strong Markov processes, DAN113, 2 (1957), 261-263

 

  1. Jump Markov processes, TV3, 1 (1958), 41-60

 

  1. New methods in the theory of Markov processes, Proceedings of the Third All-Union Congress of Mathematicians, Vol. 3, Moscow (1959), 334-342

 

  1. One-dimensional continuous strong Markov processes, TV4, 1 (1959), 3-54

 

  1. Intrinsic topology and excessive functions connected with a Markov process, DAN127 (1959), 17-19


{Selected Transl. in Math. Statistics and Probability, Vol. 3, 327-330}

  1. Linear algebra, In Mathematics in the USSR for 40 years, Vol. 1,207-212; GIFML, Moscow, 1959

 

  1. Lie groups, In Mathematics in the USSR for 40 years Vol. 1, 213-227; GIFML, Moscow 1959

 

  1. Markov processes and related problems of analysis, UMN15, 2 (92) (1960), 3-24,


{Hungarian transl. Magyar Tud. Acad.Mat.Fiz.Oszt.Kozl.17 1967, 231-251}

  1. Markov processes and their subprocesses, Proceedings of All-Union Conference on Probability Theory and Math. Statistics (Erevan, 1958), 223-235; Izdat. Akad. Nauk. Armyan. SSR, Erevan, 1960
  1. On some transformations of Markov processes, DAN133, 2 (1960), 269-272

 

  1. Additive functionals of the Wiener process determined by stochastic integrals, TV5, 4 (1960), 441-452

 

  1. Topologies associated with a Markov process and the strong Markov property (with I. V. Girsanov), TV5, 3 (1960), 375

 

  1. Random walks on groups with a finite number of generators (with M. B. Malyutov), DAN137, 5 (1961), 1042-1045

 

  1. Transformations of Markov processes connected with additive functions, Proc. 4th Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1960), vol. 2, 117-142; University of California Press, Berkeley, Calif.

 

  1. Non-negative eigenfunctions of the Laplace-Beltrami operator and Brownian motion in certain symmetric spaces, DAN141, 2 (1961), 288-292

 

  1. Brownian motion with killing measure mu and speed measure nu, DAN144, 3 (1962), 483-486

 

  1. Markov processes and problems in analysis, Proc. Intern. Congress of Mathematicians (Stockholm, 1962), pp 36-58; Inst. Mittag-Leffler, Djursholm, 1963


{Amer. Math. Soc. Transl., Series 2, Vol. 31, 1-24}

  1. Optimal choice of the stopping time of a Markov process, DAN150, 2 (1963), 238-240

 

  1. Some problems of the theory of differential equations connected with Markov processes, Outlines Joint Soviet-American Sympos. Partial Differential Equations (Novosibirsk, 1963), 67-72; Academ. Sci. USSR, Siberian Branch, Moscow 1963

 

  1. Non-negative solutions of a boundary value problem with oblique derivative, DAN157, 5 (1964), 1028-1030

 

  1. Martin boundary and non-negative solutions of a boundary value problem with oblique derivative, UMN19, 5 (119) (1964), 3-50,


Letter to the Editor 19, 6 (120), 255-256

  1. Martin boundaries, Winter School of Theory of Probability and Math. Statistics (Uzhgorod, 1964), 87-124; Izdat. Akad. Nauk Ukrain. SSR, Kiev, 1964

 

  1. Controlled random sequences, TV10, 1 (1965), 3-18

 

  1. Martin boundary and positive solutions of some boundary value problems, Annales de l'Institut Fourier (Grenoble)15, 1 (1965), 275-282
  1. Brownian motion in certain symmetric spaces and non-negative eigenfunctions of the Laplace-Beltrami operator, IAN30, 2 (1966), 455-478


{Amer. Math. Soc. Transl., Series 2, 72 (1968), 203-228}

  1. General boundary conditions for Markov processes with denumerable set of states, International Congress of Mathematicians (Moscow, 1966), Abstracts of Short Communications, Section 11, 35-36

 

  1. General additional conditions for a boundary value problem with oblique derivative, DAN168, 4 (1966), 737-739

 

  1. General boundary conditions for denumerable Markov processes, DAN172, 2 (1967), 258-261

 

  1. General boundary conditions for denumerable Markov processes, TV12, 2 (1967), 222-257;


Letter to the Editor 13, 2 (1967), 379

  1. General lateral conditions for some diffusion processes, Proc. 5th Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66; Vol.2, Part 2, 17-49; Univ. of California Press, Berkeley, Calif. 1967

 

  1. Diffusion of tensors, DAN179, 6 (1968), 1264-1267


{9,2, 532-535}

  1. Sufficient statistics for the optimal stopping problem, TV13, 1 (1968), 150-152


Letter to the Editor TV13, 4 (1968), 755

  1. On the origins of the wanderings of Markov processes (with A. A. Yushkevich), TV13, 3 (1968), 490-493

 

  1. On extensions of a Markov process TV13, 4 (1968), 708-713

 

  1. Martin boundaries, The Fourth Summer School (Katsiveli, 1966), 5-41, Naukova Dumka, Kiev 1968

 

  1. A game version of an optimal stopping problem, DAN185, 1 (1969), 16-19


{10,2, 270-274}

  1. Boundary theory for Markov processes (discrete case), UMN24, 2 (146) (1969), 3-42


{24, 2, 1-42}

  1. Exit space of a Markov process, UMN24, 4 (148) (1969), 89-152 {24, 4, 89-157}

 

  1. Excessive functions and the exit-space of a Markov process, TV15, 1 (1970), 38-55

 

  1. Classes of similar Markov processes and corresponding exit and entrance spaces, J. Sci., Univ. Tokyo, Sec. 117, 1-2 (1970), 87-100

 

  1. Excessive measures and entrance laws for a Markov process, MSb84, 2 (126) (1971), 218-253


{13, 2, 209-246}

  1. Initial and final behaviour of the trajectories of Markov processes, UMN26, 4 (160) (1971), 153-172


{26, 4 165-185}

  1. Wanderings of a Markov process, TV16, 3 (1971), 409-436


{16, 401-428}

  1. Entrance and exit spaces for a Markov Process, Actes du Congr�s International des Math�maticiens (Nice, 1970), Tome 2, 507-512; Gauthier-Villars, Paris, 1971

 

  1. Supermartingales with random birth times, UMN26, 6 (162), 1971, 241-242

 

  1. Some probability models for an expanding economy, DAN200 (1971), 523-525


{ 12 , 5, 1422-1425}

  1. Optimal control for a sequence of sums of independent random variables, Ekonom. i Mat. Metody7, 6 (1971), 901-903

 

  1. Integral representation of excessive measures and excessive functions, UMN27, 1 (163) (1972), 43-80


{ 27, 1, 43-84}

  1. Stochastic concave dynamic programming, MSb87 (129), 4 (1972), 490-503


{16, 4, 501-515}

  1. Regular Markov processes, UMN28, 2 (170) (1973), 35-64


{28, 2, 33-64}

  1. Duality in the theory of Markov process, International Conference on Probability Theory and Mathematical Statistics (Vilnius, 1973), Abstracts of Communications, Vol. 1, 213-216

 

  1. Optimal programs and stimulating prices in the stochastic models of economic growth, Math. Models in Economics ( Proc. Sympos. and Conf. on von Neumann Models, Warsaw, 1972) J. \Lo\'s and M. W. \Lo\'s, eds, pp. 207-218; North-Holland, Amsterdam; Elsevier, New York; PWN, Warszawa, 1974

 

  1. Determining functions of Markov processes and corresponding dual regular classes (with S. E. Kuznetsov), DAN214, 1 (1974), 25-28


{15, 1 20-23}

  1. Additive functionals of Markov processes and their spectral measures, DAN214, 6 (1974), 1241-1244


{15, 1, 330-334}

  1. Markov representations of stochastic systems, DAN218 (1974), 1009-1012


{15, 5 1442-1446}

  1. Markov representations of stochastic systems UMN30, 1, (181) (1975), 61-99


{30, 1 64-104}

  1. Stochastic dynamical models of economic equilibrium, Proc. of the International Congress of Mathematicians (Vancouver, BC, 1974), Vol. 2, 509-515; Canad. Math. Congress, Montreal Que, 1975

 

  1. On preference relations under uncertainty (with A. I. Ovseevich), Ekonomika i Mat. Metody 11, 2 (1975), 393-395

 

  1. Additive functionals of Markov processes and stochastic systems, Collection of articles dedicated to Marcel Brelot on the occasion of his 70th birthday, Ann. Inst. Fourier (Grenoble)25, 3-4 (1975), 177-200


Correction: 26 (1976), no.1, 1 loose p.

  1. Regular conditional mathematical expectations of correspondences (with I. V. Evstingneev), TV21, 2 (1976), 334-347

 

  1. Economic equilibrium under uncertainity, Computing Equilibria, How and Why (Proc. Internat. Conf. Comput. Centre, Polish Acad. Sci. Torun, 1974), J. \Lo's and M. W. \Lo's, eds, pp. 41-60; PWN (1976); Warszawa; North-Holland, Amsterdam, 1976.

 

  1. On a new approach to Markov processes, Proceedings of the Third Japan-USSR Symposium on Probability Theory (Tashkent, 1975), pp. 42-64. Lecture Notes in Math., vol. 550, Springer, Berlin 1976.

 

  1. Markov systems and their additive functionals, Annals of Probability5 (1977), 653-677

 

  1. Sufficient statistics and extreme points, Ann. Probab. 6 (1978), 705-730.


{Chinese transl.Yingyong Shuxue yu Jisuan Shuxue 1980, no. 6, 48-65}

  1. On duality for Markov processes, Stochastic analysis (Proc. Internat. Conf. Northwestern Univ., Evanston, Ill, 1978) , A. Friedman and M. Pinsky, eds, pp. 63-77; Academic Press, New York-London, 1978.

 

  1. Minimal excessive measures and functions, Trans. Amer. Math. Soc.258 (1980), 217-244

 

  1. Markov processes and random fields, Bull. Amer. Math. Soc. (N. S.)3, (1980) no.3, 975-999

 

  1. Markov processes, random fields and Dirichlet spaces, Physics Report77, 3 (1980), 239-247

 

  1. Additive functionals of several time-reversible Markov processes, J. Funct. Anal.42, (1980), no. 1, 64-101

 

  1. Harmonic functions associated with several Markov processes, Adv. in Appl. Math.2 (1981), 260-283

 

  1. Green's and Dirichlet spaces associated with fine Markov processes, J. Funct. Anal.47 (1982), no.3, 381-418

 

  1. Green's and Dirichlet spaces for a symmetric Markov transition functions, Probability, Statistics and Analysis, J. F. C. Kingman and G. E. H. Reuter, eds; pp. 79-98;, London Math. Soc. Lecture Note Ser. 79; Cambridge University Press, Cambridge-New York, 1983.

 

  1. Stochastic waves (with R. J. Vanderbei), Trans. Amer. Math. Soc.275 (1983),no.2 771-779

 

  1. Markov processes as a tool in field theory, J. Funct. Anal.50, (1983), no.2, 167-187

 

  1. Gaussian random fields and Gaussian evolutions, Theory and Applications of Random fields (Bangalore, 1982), G. Kallianpur, ed.,pp. 28-39; Lecture Notes in Control and Information Sci. 49, Springer, Berlin-New York, 1983.

 

  1. Symmetric statistics, Poisson point processes and multiple Wiener integrals (with A. Mandelbaum), Ann. Statist.11, (1983),no.3 739-745

 

  1. Gaussian and non-Gaussian random fields associated with Markov processes, J. Funct. Anal.55 (1984), no. 3, 344-376

 

  1. Polynomials of the occupation field and related random fields, J. Funct. Anal.58 (1984), no.1 20-52

 

  1. Local times and quantum fields Seminar on Stochastic Processes (Gainsville, Fla.) E. Cinlar, K. L. Chung, R. K. Getoor, eds, pp. 69-83, Birkh�user, Boston, 1984.

 

  1. An application of flows to time shift and time reversal in stochastic processes, Trans. Amer. Math. Soc.287 (1985), no.2, 613-619

 

  1. Random fields associated with multiple points of the Brownian motion, J. Funct. Anal.62 (1985), no.3, 397-434

 

  1. Additive functionals and entrance laws (with R. K. Getoor), J. Funct. Anal.62 (1985), 221-265

 

  1. Multiple path integals, Adv. in Appl. Math.7 (1986), no. 2, 205-219

 

  1. Generalized random fields related to self-intersections of the Brownian motion, Proc. Nat. Acad. Sci. USA83 (1986), no.11 3573-3576

 

  1. Functionals associated with self-intersections of the planar Brownian motion, S�minaire de Probabilit�s, XX, 1984/85, pp. 553-571, J. Az�ma, M. Yor, eds; Lecture Notes in Math., 1204, Springer, Berlin/New York, 1986.

 

  1. Self-intersection local times, occupation fields and stochastic integrals, Adv. in Math.65 (1987), no. 3, 254-271.

 

  1. Stochastic processes on random domains (with P. J. Fitzsimmons), Ann. Inst. H. Poincar� Probab. Statist. 23 (1987),no. 2, suppl. 379-396.

 

  1. Regularized self-intersection local times of planar Brownian motion, Ann. Probab.16 (1988), no. 1, 58-74
  1. Self-intersection gauge for random walks and for Brownian motion, Ann. Probab.16 (1988), no. 1, 1-57

 

  1. Representation for functionals of superprocesses by multiple stochastic integrals, with applications to self-intersectional local times, Colloque Paul L�vy sur le Processus Stochastiques (Palaiseau, 1987). Ast�risque157-158 (1988), 147-171

 

  1. Superprocesses and their linear additive functionals, Trans. Amer. Math. Soc.314 (1989), 255-282

 

  1. Three classes of infinite dimensional diffusions, J. Funct. Anal.86 (1989), no.1 75-110

 

  1. Kolmogorov and theory of Markov processes Ann. Probab.17 (1989), no. 3, 822-832