Long-term behavior for superprocesses over a stochastic flow
- Xiong, Jie
2010 Mathematics Subject Classification
- 60G57 60H15 60J80
- Superprocess, stochastic flow, log-Laplace equation, long-term behavior
We study the limit of a superprocess controlled by a stochastic flow as $ttoinfty$. It is proved that when $dle 2$, 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  and studied by this author  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.