Lebesgue approximation of $(2,β)$-superprocesses

Details Lebesgue approximation of $(2,β)$-superprocesses Lebesgue approximation of $(2,β)$-superprocesses

2012-01-31

arxiv.org/abs/1201.6437v2

Mathematics

Probability

arXiv admin note: text overlap with arXiv:0901.2840

Scientific paper

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.

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