School of Operations Research
220 Rhodes Hall
A new book "Stochastic Processes and Long
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 risk models. I am also interested in the extremal behavour of stochastic proceses and random fields, in particular in extremes of models used in climate, as well as statistical analysis of extremes in climate data.
My other areas of interest include self-similar (fractal-like) stochastic processes, stable and other infinitely divisible processes, geometry of the excursion sets of random fields, scale free random graphs, and connections between probability and ergodic theoy.
Last revised: 10/23/2013