Electronic Communications in Probability

Long-term behavior for superprocesses over a stochastic flow

Jie Xiong

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We study the limit of a superprocess controlled by a stochastic flow as $t\to\infty$. It is proved that when $d \le 2$, this process suffers long-time local extinction; when $d\ge 3$, 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.

Article information

Electron. Commun. Probab., Volume 9 (2004), paper no. 5, 36-52.

Accepted: 7 April 2004
First available in Project Euclid: 26 May 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G57: Random measures 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Superprocess stochastic flow log-Laplace equation long-term behavior

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Xiong, Jie. Long-term behavior for superprocesses over a stochastic flow. Electron. Commun. Probab. 9 (2004), paper no. 5, 36--52. doi:10.1214/ECP.v9-1081. https://projecteuclid.org/euclid.ecp/1464286685

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