Cluster continuous time random walks
Volume 205 / 2011
Studia Mathematica 205 (2011), 13-30
MSC: Primary 60G50, 60F17, 60G18, 60G22; Secondary 60H30, 82C31.
DOI: 10.4064/sm205-1-2
Abstract
In a continuous time random walk (CTRW), a random waiting time precedes each random jump. The CTRW model is useful in physics, to model diffusing particles. Its scaling limit is a time-changed process, whose densities solve an anomalous diffusion equation. This paper develops limit theory and governing equations for cluster CTRW, in which a random number of jumps cluster together into a single jump. The clustering introduces a dependence between the waiting times and jumps that significantly affects the asymptotic limit. Vector jumps are considered, along with oracle CTRW, where the process anticipates the next jump.
