Time-Changed Processes and Cauchy Problems

Dr. Erkan Nane

Department of Mathematics and Statistics
Auburn University

11 November 2011
Shelby Center 218
3:00 (Refreshements at 2:30)

Abstract

In a continuous time random walk (CTRW), each random jump follows a random waiting time. CTRW scaling limits are time-changed processes that model anomalous diffusion. The outer process describes particle jumps, and the non-Markovian inner process (or time change) accounts for waiting times between jumps.

In this talk, I will consider fractal properties of the sample functions of a time-changed process, and study some general results on the Hausdorff dimensions of its range and graph. I will also talk about the Cauchy problems for CTRW limit processes. Fractional Cauchy problems or Cauchy problems involving the powers of the generator of the Markov processes are obtained. In some special cases, the equivalence of these two types of Cauchy problems is established.