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Quenched convergence of a sequence of superprocesses in among Poissonian obstacles

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  • Véber, Amandine

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.

Suggested Citation

  • Véber, Amandine, 2009. "Quenched convergence of a sequence of superprocesses in among Poissonian obstacles," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2598-2624, August.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:8:p:2598-2624
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    References listed on IDEAS

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    1. Sznitman, A. S., 1987. "Some bounds and limiting results for the measure of Wiener sausage of small radius associated with elliptic diffusions," Stochastic Processes and their Applications, Elsevier, vol. 25, pages 1-25.
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