Limit theorems for a class of critical superprocesses with stable branching

Yan-Xia Ren, Renming Song and Zhenyao Sun

Stochastic Processes and their Applications, 2020, vol. 130, issue 7, 4358-4391

Abstract: We consider a critical superprocess {X;Pμ} with general spatial motion and spatially dependent stable branching mechanism with lowest stable index γ0>1. We first show that, under some conditions, Pμ(|Xt|≠0) converges to 0 as t→∞ and is regularly varying with index (γ0−1)−1. Then we show that, for a large class of non-negative testing functions f, the distribution of {Xt(f);Pμ(⋅|‖Xt‖≠0)}, after appropriate rescaling, converges weakly to a positive random variable z(γ0−1) with Laplace transform E[e−uz(γ0−1)]=1−(1+u−(γ0−1))−1∕(γ0−1).

Keywords: Critical superprocess; Stable branching; Scaling limit; Intrinsic ultracontractivity; Regular variation (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2020.01.001

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