Scaling limits of coupled continuous time random walks and residual order statistics through marked point processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Barczyk, A.¹  Kern, P.¹ 

[1] Univ Dusseldorf, Math Inst, D-40225 Dusseldorf, Germany

关键词: Continuous time random walk;    Operator stable law;    Levy process;    Marked point process;    Order statistics;    Series representation;   

DOI  :  10.1016/j.spa.2012.10.013

来源: Elsevier

【 摘 要 】

A continuous time random walk (CTRW) is a random walk in which both spatial changes represented by jumps and waiting times between the jumps are random. The CTRW is coupled if a jump and its preceding or following waiting time are dependent random variables (r.v.), respectively. The aim of this paper is to explain the occurrence of different limit processes for CTRWs with forward- or backward-coupling in Straka and Henry (2011) [37] using marked point processes. We also establish a series representation for the different limits. The methods used also allow us to solve an open problem concerning residual order statistics by LePage (1981) [20]. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free