Particle representations of superprocesses with dependent motions

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:120

Article

Temple, Kathryn E.

关键词: Particle representation;    Superprocess;    Dependent motions;    Coalescing Brownian motion;    Interacting Brownian flow;   

DOI  :  10.1016/j.spa.2010.06.005

来源: Elsevier

【 摘 要 】

We establish Donnelly Kurtz-type particle representations for a class of superprocesses with dependent spatial motions, and for a sequence of such superprocesses we prove convergence of the finite-dimensional distributions given convergence of the motion processes. As special cases, we construct a superprocess with coalescing spatial motion (SCSM) and a superprocess with dependent spatial motion (SDSM), where the underlying motion processes are one-dimensional coalescing and dependent Brownian motions, respectively. Under suitable conditions on the functions governing the interactions, we show convergence in distribution in D(P(R))[0,infinity) of a sequence of SDSMs to an SCSM. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free