Open Access
October, 1995 The Support of Measure-Valued Branching Processes in a Random Environment
D. Dawson, Y. Li, C. Mueller
Ann. Probab. 23(4): 1692-1718 (October, 1995). DOI: 10.1214/aop/1176987799


We consider the one-dimensional catalytic branching process introduced by Dawson and Fleischmann, which is a modification of the super-Brownian motion. The catalysts are given by a nonnegative infinitely divisible random measure with independent increments. We give sufficient conditions for the global support of the process to be compact, and sufficient conditions for noncompact global support. Since the catalytic process is related to the heat equation, compact support may be surprising. On the other hand, the super-Brownian motion has compact global support. We find that all nonnegative stable random measures lead to compact global support, and we give an example of a very rarified Levy process which leads to noncompact global support.


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D. Dawson. Y. Li. C. Mueller. "The Support of Measure-Valued Branching Processes in a Random Environment." Ann. Probab. 23 (4) 1692 - 1718, October, 1995.


Published: October, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0853.60065
MathSciNet: MR1379164
Digital Object Identifier: 10.1214/aop/1176987799

Primary: 60H15
Secondary: 35R60

Keywords: branching processes , Levy processes , Stochastic partial differential equations , Support

Rights: Copyright © 1995 Institute of Mathematical Statistics

Vol.23 • No. 4 • October, 1995
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