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Mutually interacting superprocesses with migration

Part of: Stochastic analysis Special processes Markov processes

Published online by Cambridge University Press:  11 July 2022

Lina Ji Open the ORCID record for Lina Ji [Opens in a new window] ,
Huili Liu Open the ORCID record for Huili Liu [Opens in a new window]  and
Jie Xiong
Lina Ji*
Affiliation:
Shenzhen MSU-BIT University
Huili Liu*
Affiliation:
Hebei Normal University
Jie Xiong*
Affiliation:
Southern University of Science and Technology
*
*Postal address: Faculty of Computational Mathematics and Cybernetics, Shenzhen MSU-BIT University, Shenzhen, Guangdong, 518172, China.
**Postal address: School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, Hebei, 050024, China. Email address: liuhuili@hebtu.edu.cn
***Postal address: Department of Mathematics & National Center for Applied Mathematics (Shenzhen), Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China.
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Abstract

A system of mutually interacting superprocesses with migration is constructed as the limit of a sequence of branching particle systems arising from population models. The uniqueness in law of the superprocesses is established using the pathwise uniqueness of a system of stochastic partial differential equations, which is satisfied by the corresponding system of distribution function-valued processes.

Keywords

Distribution function-valuedMartingale problemsuperprocessstochastic partial differential equationwell-posedness

MSC classification

Primary: 60J68: Superprocesses
Secondary: 60H15: Stochastic partial differential equations 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Original Article
Information
Journal of Applied Probability , Volume 59 , Issue 3 , September 2022 , pp. 904 - 929
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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