Lebesgue approximation of $(2,\beta)$-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


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