Journal of Statistical Physics

, Volume 81, Issue 3–4, pp 777–792 | Cite as

Asymptotic distributions of continuous-time random walks: A probabilistic approach

  • Marcin Kotulski


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.

Key Words

Random walks coupled memory asymptotic distributions Lévy-stable distributions 


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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Marcin Kotulski
    • 1
  1. 1.Hugo Steinhaus Center for Stochastic MethodsTechnical University of WrocławWrocławPoland

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