 Quenched convergence of a sequence of superprocesses in among Poissonian obstaclesAmandine Véber Stochastic Processes and their Applications, 2009, vol. 119, issue 8, 2598-2624 Abstract: 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 of the obstacles, and -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)=u2+[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. Keywords: Super-Brownian; motion; Random; obstacles; Quenched; convergence; Brownian; motion; Wiener; sausage (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:119:y:2009:i:8:p:2598-2624 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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