Lebesgue approximation of (2,β)-superprocesses

2012/01/31 by Xin He, He, Xin
Mathematics · #60J68 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60J68

paper · pdf · doi:10.48550/arxiv.1201.6437

arXiv admin note: text overlap with arXiv:0901.2840

arxiv created 2012/02/01 · arxiv updated 2012/02/02

Abstract

Let ξ=(ξ_t) be a locally finite (2,β)-superprocess in \RR^d with β<1 and d>2/β. Then for any fixed t>0, the random measure ξ_t can be a.s. approximated by suitably normalized restrictions of Lebesgue measure to the ε-neighborhoods of \rm supp ξ_t. This extends the Lebesgue approximation of Dawson-Watanabe superprocesses. Our proof is based on a truncation of (α,β)-superprocesses and uses bounds and asymptotics of hitting probabilities.

Citations

• Some local approximations of Dawson–Watanabe superprocesses

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