My interest lies both in probability theory and in its various applications. A very important area is that of stochastic modeling, and I am especially interested in "non-standard" models, in particular those exhibiting heavy tails and/or long-range dependence. These models behave very differently from the "usual" models that are typically based on Gaussian or Markov stochastic processes. Both heavy tails and long-range dependence are observed in financial processes, teletraffic processes and many other processes. Since many classical statistical tools break down in the presence of long-range dependence and/or absence of Gaussianity, it is very important to understand how "non-standard" models behave, how one simulates them, how one estimates their parameters, and how one predicts their behavior in the future. I am looking closely, in particular, at certain financial and queueing models. I am also interested in extremes in climate.
My other areas of interest include stochastic processes in finance and risk theory, self-similar (fractal-like) stochastic processes, extrema of stochastic processes, zero-one laws, positive and negative dependence in stochastic processes, stable and other infinitely divisible processes and level crossings of stochastic processes.
Current Research Projects
EXTREMES OF STOCHASTIC PROCESSES AND Intrinsic location functionals of stationary processesIntrinsic location functionals of stationary processesIntrinsic location functionals of stationary processesIntrinsic location functionals of stationary processesIntrinsic location functionals of stationary processes RANDOM FIELDS: NEW DIRECTIONS (National Science Foundation)
ROBUST MODELING OF COMPLEX SYSTEMS WITH HEAVY TAILS AND LONG MEMORY (Army Research Office)
NON-GAUSSIAN RANDOM FIELDS, EXCURSIONS AND GEOMETRY (National Security Agency)
DECADAL PREDICTABILITY OF EXTREME EVENTS: IMPACT OF A MODEL ERROR REPRESENTATION AND NUMERICAL RESOLUTIONS (National Science Foundation)