Superprocesses with spatial interactions in a random medium

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Gill, Hardeep S.

关键词: Dawson-Watanabe superprocesses;    Interactive measure-valued diffusions;    Historical super-Brownian motion;    Stochastic processes;    Martingale problem;   

DOI  :  10.1016/j.spa.2009.09.009

来源: Elsevier

【 摘 要 】

We construct a class of interactive measure-valued diffusions driven by a historical super-Brownian motion and an independent white noise by solving a certain stochastic equation. In doing so, we show that the approach of Perkins (2002) [3] can be used to study the problem examined by Dawson et al. (200 1) [1]. This unifies and extends both Dawson et al. (2001) [1] and Perkins (2002) [3] and establishes a new class of measure-valued diffusions. The existence and pathwise uniqueness of the Solutions are proved, and the solutions are shown to satisfy the natural martingale problem. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free