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MATH 778 —
Spring 2000
Markov Processes
| Instructor: |
Eugene Dynkin |
| Time: |
TR 10:10-11:25 |
| Room: |
MT 206 |
- Brownian motion. Additive functionals and transformations based on
them (killing, random time change, Girsanov's transformation). Local
times and self-intersection local times. A general continuous strong
Markov process in R.
- Three methods of constructing a diffusion: via fundamental solution
of the heat equation, by Ito's equation, by solving a martingale problem.
- The first boundary value problem for linear elliptic and parabolic
equation in an arbitrary domain. Analytic solution by the Perron-Wiener-Brelot
method. Probabilistic solution. Martin boundary. Stochastic boundary
values.
- Exceptional sets in analysis and in probability. Probabilistic theory
of potential.
- Infinitely divisible random measures.
- Branching exit Markov systems.
- Superdiffusions and semilinear elliptic and parabolic equations.
Removable singularities in a domain and on its boundary — relation
to hitting probabilities by a superdiffusion. Characterization of positive
solutions by their trace on the boundary.
I will avoid generalities and technicalities and concentrate on principal
ideas and concrete problems. Prerequisites: the Lebesgue integration
theory and an interest in probability theory.
Last modified:
April 7, 2003
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