Quenched convergence of a sequence of superprocesses in Rd among Poissonian obstacles

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Veber, Amandine

关键词: Super-Brownian motion;    Random obstacles;    Quenched convergence;    Brownian motion;    Wiener sausage;   

DOI  :  10.1016/j.spa.2009.01.004

来源: Elsevier

【 摘 要 】

We prove a convergence theorem for a sequence of super-Brownian motions moving among hard Poissonian obstacles, when the intensity of the obstacles grows to infinity but their diameters shrink to zero in an appropriate manner. The superprocesses are shown to converge in probability for the law P of the obstacles, and P-almost surely for a subsequence, towards a superprocess with underlying spatial motion given by Brownian motion and (inhomogeneous) branching mechanism psi(u, x) of the form psi (u, x) = u(2) + kappa(x)u, where kappa(x) depends on the density of the obstacles. This work draws on similar questions for a single Brownian motion. In the course of the proof, we establish precise estimates for integrals of functions over the Wiener sausage, which are of independent interest. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

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