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February 2001 Superprocesses of stochastic flows
Zhi-Ming Ma, Kai-Nan Xiang
Ann. Probab. 29(1): 317-343 (February 2001). DOI: 10.1214/aop/1008956332


We construct a continuous superprocess X on M (R d) which is the unique weak Feller extension of the empirical process of consistent k-point motions generated by a family of differential operators. The process X differs from known Dawson–Watanabe type, Fleming–Viot type and Ornstein–Uhlenbeck type superprocesses. This new type of superprocess provides a connection between stochastic flows and measure-valued processes, and determines a stochastic coalescence which is similar to those of Smoluchowski. Moreover, the support of X describes how an initial measure on R d is transported under the flow. As an example, the process realizes a viewpoint of Darling about the isotropic stochastic flows under certain conditions.


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Zhi-Ming Ma. Kai-Nan Xiang. "Superprocesses of stochastic flows." Ann. Probab. 29 (1) 317 - 343, February 2001.


Published: February 2001
First available in Project Euclid: 21 December 2001

zbMATH: 1015.60063
MathSciNet: MR1825152
Digital Object Identifier: 10.1214/aop/1008956332

Primary: 60G57 , 60H15 , 60J25

Keywords: Measure-valued process , Stochastic coalescence , stochastic flow

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.29 • No. 1 • February 2001
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