Lagging and leading coupled continuous time random walks, renewal times and their joint limits

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:121

Article

Straka, P.¹  Henry, B. I.¹ 

[1] Univ New S Wales, Sch Math & Stat, Dept Appl Math, Sydney, NSW 2052, Australia

关键词: Continuous time random walk;    Stochastic process limit;    Levy process;    Time-change;    Subordination;    Triangular array;    Renewal times;    Skorokhod space;    Subdiffusion;   

DOI  :  10.1016/j.spa.2010.10.003

来源: Elsevier

【 摘 要 】

Subordinating a random walk to a renewal process yields a continuous time random walk (CTRW), which models diffusion and anomalous diffusion. Transition densities of scaling limits of power law CTRWs have been shown to solve fractional Fokker-Planck equations. We consider limits of CTRWs which arise when both waiting times and jumps are taken from an infinitesimal triangular array. Two different limit processes are identified when waiting times precede jumps or follow jumps, respectively, together with two limit processes corresponding to the renewal times. We calculate the joint law of all four limit processes evaluated at a fixed time t. (c) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free