Cluster continuous time random walks

Agnieszka Jurlewicz, Mark M. Meerschaert, and Hans-Peter Scheffler. "Cluster continuous time random walks." Studia Mathematica 205.1 (2011): 13-30. <http://eudml.org/doc/285699>.

@article{AgnieszkaJurlewicz2011,
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.},
author = {Agnieszka Jurlewicz, Mark M. Meerschaert, Hans-Peter Scheffler},
journal = {Studia Mathematica},
keywords = {continuous time random walk; random number of jumps; operator stable law; scaling limit; equations with fractional partial derivatives},
language = {eng},
number = {1},
pages = {13-30},
title = {Cluster continuous time random walks},
url = {http://eudml.org/doc/285699},
volume = {205},
year = {2011},
}

TY - JOUR
AU - Agnieszka Jurlewicz
AU - Mark M. Meerschaert
AU - Hans-Peter Scheffler
TI - Cluster continuous time random walks
JO - Studia Mathematica
PY - 2011
VL - 205
IS - 1
SP - 13
EP - 30
AB - 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.
LA - eng
KW - continuous time random walk; random number of jumps; operator stable law; scaling limit; equations with fractional partial derivatives
UR - http://eudml.org/doc/285699
ER -