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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.