Operations Research and Information Engineering
Research Interests: His research interests lie both in probability theory and in its various applications. A very important area is that of stochastic modeling, and he is 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. He is interested in interaction of toplogy with probability theory; applications are, among others, in medicine and cosmology. A major area of interest is studying and modeling extremes in climate and understanding, in particular, whether, in fact, extremes in climate grow faster than the averages. He is looking closely, in particular, at certain financial and queueing models. Other areas of interest include 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.