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

2011/02/17 by Rong-Li Liu, Liu, Rong-Li, Yan-Xia Ren +3
Mathematics · #60G55 #60G57 #60J68 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G55 #msc:60G57 #msc:60J68

paper · pdf · doi:10.48550/arxiv.1102.3668

arxiv created 2011/02/17 · arxiv updated 2011/02/18

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 ∂_t u_t=L u_t+βu_t-ψ(u_t) on a bounded domain D in \R^d, where L is the generator of the underlying diffusion and the branching mechanism ψ(x,λ)=1/2α(x)λ²+∫₀^∞ (e^-λr-1+λr)n(x, \rm dr) satisfies sup_{x∈ D}∫₀^∞ (r\wedge r²) n(x,\rm dr)<∞.

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