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January, 1992 The Behavior of Superprocesses Near Extinction
Roger Tribe
Ann. Probab. 20(1): 286-311 (January, 1992). DOI: 10.1214/aop/1176989927


In this paper we use a martingale problem characterization to study the behavior of finite measure valued superprocesses with a variety of spatial motions. In general the superprocess, when normalized to be a probability, will converge to a point mass at its extinction time. For some spatial motions we prove that there are times near extinction at which the closed support of the process is concentrated near one point. We obtain a Tanaka formula for the measure of a half space under a one dimensional symmetric stable superprocess of index $\alpha$ and we show this process fails to be a semimartingale if $1 < \alpha \leq 2$.


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Roger Tribe. "The Behavior of Superprocesses Near Extinction." Ann. Probab. 20 (1) 286 - 311, January, 1992.


Published: January, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0749.60046
MathSciNet: MR1143421
Digital Object Identifier: 10.1214/aop/1176989927

Primary: 60G57
Secondary: 60G44

Keywords: measure valued , Superprocess , Tanaka formula

Rights: Copyright © 1992 Institute of Mathematical Statistics


Vol.20 • No. 1 • January, 1992
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