Lebesgue approximation of (2,β)-superprocesses

Xin He

Stochastic Processes and their Applications, 2013, vol. 123, issue 5, 1802-1819

Abstract: 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.

Keywords: Super-Brownian motion; Branching mechanism; Symmetric stable process; Historical cluster; Hitting probability; Hitting bound; Hitting asymptotic; Local finiteness; Local extinction; Neighborhood measure (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2013.01.010

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