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October 2001 Branching Exit Markov Systems and Superprocesses
E.B. Dynkin
Ann. Probab. 29(4): 1833-1858 (October 2001). DOI: 10.1214/aop/1015345774

Abstract

Superprocesses (under the name continuous state branchingprocesses) appeared, first, in a pioneering work of S.Watanabe [J. Math. Kyoto Univ. 8 (1968)141 –167 ]. Deep results on paths of the super-Brownian motion were obtained by Dawson, Perkins, Le Gall and others.

In earlier papers, a superprocess was interpreted as a Markov process $X_t$ in the space of measures. This is not sufficient for a probabilistic approach to boundary value problems. A reacher model based on the concept of exit measures was introduced by E.B.Dynkin [Probab. Theory Related Fields 89 (1991) 89 –115 ]. A model of a superprocess as a system of exit measures from time-space open sets was systematically developed in 1993 [E.B. Dynkin, Ann.Probab. 21 (1993)1185 –1262 ]. In particular, branchingand Markov properties of such a system were established and used to investigate partial differential equations. In the present paper, we show that the entire theory of superprocesses can be deduced from these properties.

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E.B. Dynkin. "Branching Exit Markov Systems and Superprocesses." Ann. Probab. 29 (4) 1833 - 1858, October 2001. https://doi.org/10.1214/aop/1015345774

Information

Published: October 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1014.60079
MathSciNet: MR1880244
Digital Object Identifier: 10.1214/aop/1015345774

Subjects:
Primary: 60J60 , 60J80

Keywords: Branching particle systems , branching property , exit measures , Markov property , Superprocesses , transition operators

Rights: Copyright © 2001 Institute of Mathematical Statistics

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Vol.29 • No. 4 • October 2001
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