Some Recent Results on Stable Processes

Dr. Renming Song

Department of Mathematics
University of Illinois at Urbana-Champaign

3:00 Friday, 27 March 2009
219 Shelby Center

Abstract

Symmetric α-stable processes (α in [0, 2]) form one of the most important class of stochastic processes, and when α = 2, the symmetric α-stable process reduces to a Brownian motion. Just like Brownian motion is related to the Laplacian Δ, a symmetric α-stable process is related to the fractional Laplacian −(−Δ)^α/2. Recently a lot of progress has been made in the study of symmetric stable processes and their generalizations. In this talk I will give a survey of some of these recent results.