Long-term behavior for superprocesses over a stochastic flow | Zendy

Jie Xiong | Zendy

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Long-term behavior for superprocesses over a stochastic flow

Author(s) -

Jie Xiong

Publication year - 2004

Publication title -

electronic communications in probability

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.236

H-Index - 38

ISSN - 1083-589X

DOI - 10.1214/ecp.v9-1081

Subject(s) - mathematics , term (time) , flow (mathematics) , statistical physics , econometrics , geometry , physics , quantum mechanics

We study the limit of a superprocess controlled by a stochastic ∞ow as t ! 1. It is proved that when d • 2, this process sufiers long-time local extinction; when d ‚ 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, similar to the one played by the log-Laplace equation in deriving long-term behavior for the standard super-Brownian motion.

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