Wenbo Li
University of Delaware
Title: A survey on small ball probabilities for stable processes.

The small ball probability or small deviation studies the behavior of log mu (x : ||x|| <= t) as t tend to zero for a given measure mu and a norm ||.||. In the literature, small ball probabilities of various types are studied and applied to many problems of interest under different names such as small deviation, lower tail behavior, two sided boundary crossing probabilities, the first exit probabilities, the asymptotes of Laplace transforms, etc. We will overview some of the recent developments for stable measures/processes and present various connections with other areas of probability and analysis.
©2005, Department of Mathematical Sciences
Last Modified: February 10, 2005