The Annals of Probability

Superprocesses of stochastic flows

Zhi-Ming Ma and Kai-Nan Xiang

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Abstract

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.

Article information

Source
Ann. Probab., Volume 29, Number 1 (2001), 317-343.

Dates
First available in Project Euclid: 21 December 2001

Permanent link to this document
https://projecteuclid.org/euclid.aop/1008956332

Digital Object Identifier
doi:10.1214/aop/1008956332

Mathematical Reviews number (MathSciNet)
MR1825152

Zentralblatt MATH identifier
1015.60063

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60] 60G57: Random measures 60J25: Continuous-time Markov processes on general state spaces

Keywords
Stochastic flow measure-valued process stochastic coalescence

Citation

Ma, Zhi-Ming; Xiang, Kai-Nan. Superprocesses of stochastic flows. Ann. Probab. 29 (2001), no. 1, 317--343. doi:10.1214/aop/1008956332. https://projecteuclid.org/euclid.aop/1008956332


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