WIAS Preprint No. 906, (2004)

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 [7] and studied by this author [12] 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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