Lebesgue approximation of (2,β)-superprocesses

Speaker: Xin He

Date: Thu, Jun 21, 2012

Location: PIMS, University of British Columbia

Conference: PIMS-MPrime Summer School in Probability

Subject: Mathematics, Probability

Class: Scientific

Abstract:

Let ξ=(ξt) be a locally finite (2,β)-superprocess in \RRd 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.