Cluster continuous time random walks

• Autorzy: Agnieszka Jurlewicz , Mark M. Meerschaert , Hans-Peter Scheffler
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 60G50: Sums of independent random variables; random walks
• 60F17: Functional limit theorems; invariance principles
• 60G22: Fractional processes, including fractional Brownian motion
• 82C31: Stochastic methods (Fokker-Planck, Langevin, etc.)
• 60G18: Self-similar processes
• 60H30: Applications of stochastic analysis (to PDE, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 205
• Numer: 1
• Strony: 13-30

Daty

wydano

2011

Twórcy

autor

Agnieszka Jurlewicz

• Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wrocław University of Technology, 50-370 Wrocław, Poland

autor

Mark M. Meerschaert

• Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, U.S.A.

autor

Hans-Peter Scheffler

• Fachbereich Mathematik, Universität Siegen, 57068 Siegen, Germany

Identyfikatory

DOI

10.4064/sm205-1-2