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Strong law of large number of a class of super-diffusions

By Rong-Li Liu, Yan-Xia Ren and Renming Song

Abstract

In this paper we prove that, under certain conditions, a strong law of large numbers holds for a class of super-diffusions $X$ corresponding to the evolution equation $\partial_t u_t=L u_t+\beta u_t-\psi(u_t)$ on a bounded domain $D$ in $\R^d$, where $L$ is the generator of the underlying diffusion and the branching mechanism $\psi(x,\lambda)=1/2\alpha(x)\lambda^2+\int_0^\infty (e^{-\lambda r}-1+\lambda r)n(x, {\rm d}r)$ satisfies $\sup_{x\in D}\int_0^\infty (r\wedge r^2) n(x,{\rm d}r)<\infty$

Topics: Mathematics - Probability, 60J68, 60G55, 60G57
Year: 2011
OAI identifier: oai:arXiv.org:1102.3668
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