Cluster continuous time random walks

Volume 205 / 2011

Agnieszka Jurlewicz, Mark M. Meerschaert, Hans-Peter Scheffler Studia Mathematica 205 (2011), 13-30 MSC: Primary 60G50, 60F17, 60G18, 60G22; Secondary 60H30, 82C31. DOI: 10.4064/sm205-1-2


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.


  • Agnieszka JurlewiczHugo Steinhaus Center
    Institute of Mathematics and Computer Science
    Wrocław University of Technology
    50-370 Wrocław, Poland
  • Mark M. MeerschaertDepartment of Statistics and Probability
    Michigan State University
    East Lansing, MI 48824, U.S.A.
  • Hans-Peter SchefflerFachbereich Mathematik
    Universität Siegen
    57068 Siegen, Germany

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