Limit theorems for coupled continuous time random walks.
type: Item
instance of: scholarly article
title: Limit theorems for coupled continuous time random walks.
zbMATH Open document ID: 1054.60052
author: Mark M. Meerschaert
author: Peter Kern
author: Hans-Peter Scheffler
published in: The Annals of Probability
publication date: 2004-09-15T00:00:00Z
review text: The continuous time random walk is a jump process with independent identically distributed waiting times between the jumps. Mathematically this model process, for so-called anomalous diffusion, may be interpreted as a random walk subordinated to a suitable renewal process. Usually, CTRW is regarded to be uncoupled, meaning that the random walk is independent of the subordinating renewal process. The main focus of the paper are scaling limits (large time behavior) of the coupled process whose jump sizes and waiting times are not independent random variables. The pertinent infinite mean waiting time limit, in the coupled subordination case, allows to infer a simple formula for the limiting probability distribution. Links with pseudodifferential equations are conjectured. Explicit examples of coupled and uncoupled CTRWs are elaborated.
reviewed by: Piotr Garbaczewski
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60H30
Mathematics Subject Classification ID: 82C31
zbMATH DE Number: 2100732
zbMATH Keywords: jump processes
zbMATH Keywords: waiting time
zbMATH Keywords: continuous time random walk
zbMATH Keywords: limit theorems
zbMATH Keywords: renewal process
zbMATH Keywords: Lévy walk
zbMATH Keywords: Lévy measure
zbMATH Keywords: infinitely divisible distributions
zbMATH Keywords: anomalous diffusion
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1079021462
OpenAlex ID: W2090039668
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DOI: 10.1214/AOP/1079021462
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description: scientific article; zbMATH DE number 2100732