Asymptotic distributions of continuous-time random walks: A probabilistic approach |
| |
Authors: | Marcin Kotulski |
| |
Institution: | (1) Hugo Steinhaus Center for Stochastic Methods, Technical University of Wroc aw, Wyspia skiego 27, 50-370 Wroc aw, Poland |
| |
Abstract: | We provide a systematic analysis of the possible asymptotic distributions o one-dimensional continuous-time random walks (CTRWs) by applying the limit theorems of probability theory. Biased and unbiased walks of coupled and decoupled memory are considered. In contrast to previous work concerning decoupled memory and Lévy walks, we deal also with arbitrary coupled memory and with jump densities asymmetric about its mean, obtaining asymmetric Lévy-stable limits. Suprisingly, it is found that in most cases coupled memory has no essential influence on the form of the limiting distribution. We discuss interesting properties of walks with an infinite mean waiting time between successive jumps. |
| |
Keywords: | Random walks coupled memory asymptotic distributions Lé vy-stable distributions |
本文献已被 SpringerLink 等数据库收录! |
|