Title: Boundary Trace of a Markov Process
Speaker: Professor Zhen-Qing Chen
Speaker Info: University of Washington
Given an n-dimensional symmetric Levy process X and a closed subset F in an Euclidean space, what is the trace of the Levy process on F? To better formulate it, let m be a Revuz measure of X whose support is F. The time-changed process of X by m can be regarded as the trace process of X on F. So the more precise question is: can we characterize such time-changed process?Date: Saturday, October 16, 2004
Time change is one of the most basic and very useful transformations for Markov processes, which has been studied by many authors. However a precise characterization of the time-changed process is only started very recently. In this talk, we will address the above type of questions not only for Levy processes but also for general irreducible symmetric Markov processes. We will present a complete haracterization of the quadratic (or energy) form for the time-changed process and derive its Beurling-Deny decomposition. In particular, the Levy system of the time-changed process will be determined.