Long-term behavior for superprocesses over a stochastic flow
Jie Xiong, University of Tennessee
Abstract
We study the limit of a superprocess
controlled by a stochastic flow as
$ttoinfty$. It is proved that when $d le 2$,
this process suffers long-time local extinction;
when $dge 3$, it has a limit which is persistent.
The stochastic log-Laplace equation conjectured
by Skoulakis and Adler (2001) and studied by this author
(2004) plays a key role in the proofs like the one played by
the log-Laplace equation
in deriving long-term behavior for usual super-Brownian motion.
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