Lebesgue approximation of (2,β)-superprocesses

Let ξ=(ξt) be a locally finite (2,β)-superprocess in Rd with β<1 and d>2/β. Then for any fixed t>0, the random measure ξt can be a.s. approximated by suitably normalized restrictions of Lebesgue measure to the ε-neighborhoods of suppξt. 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.

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Year of publication:	2013
Authors:	He, Xin
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 123.2013, 5, p. 1802-1819
Publisher:	Elsevier
Subject:	Super-Brownian motion \| Branching mechanism \| Symmetric stable process \| Historical cluster \| Hitting probability \| Hitting bound \| Hitting asymptotic \| Local finiteness \| Local extinction \| Neighborhood measure

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011064931