1212.1197 (Peter Straka)

Inhomogeneous and Coupled Continuous Time Random Walk Limits    [PDF]

Peter Straka

We study stochastic process limits of Continuous Time Random Walks (CTRWs) whose jumps and waiting times vary in both time and space and are possibly coupled. We prove limit theorems for the weak convergence in Skorokhod space of cadlag paths. In the case of coupled waiting times and jumps, there exist two different limit processes. These limit processes are then characterized via a tuple of coefficients, which is derived from a jump-diffusion processes in space-time. We then calculate the one-dimensional laws of these two limit processes, and show that these laws solve forward and backward Kolmogorov equations with non-local time operators. Finally, we discuss an application of our theory to the case of subdiffusion in a time-dependent force-field.

View original: http://arxiv.org/abs/1212.1197