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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm205-1-2,
author = {Agnieszka Jurlewicz and Mark M. Meerschaert and Hans-Peter Scheffler},
title = {Cluster continuous time random walks},
journal = {Studia Mathematica},
volume = {204},
year = {2011},
pages = {13-30},
zbl = {1242.60045},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm205-1-2}
}
Agnieszka Jurlewicz; Mark M. Meerschaert; Hans-Peter Scheffler. Cluster continuous time random walks. Studia Mathematica, Tome 204 (2011) pp. 13-30. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm205-1-2/