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June 2009 A class of stochastic partial differential equations for interacting superprocesses on a bounded domain
Yan-Xia Ren, Renming Song, Hao Wang
Osaka J. Math. 46(2): 373-401 (June 2009).

Abstract

A class of interacting superprocesses on $\mathbb{R}$, called superprocesses with dependent spatial motion (SDSMs), were introduced and studied in Wang [32] and Dawson et al. [9]. In the present paper, we extend this model to allow particles moving in a bounded domain in $\mathbb{R}^{d}$ with killing boundary. We show that under a proper re-scaling, a class of discrete SPDEs for the empirical measure-valued processes generated by branching particle systems subject to the same white noise converge in $L^{2}(\Omega, \mathcal{F}, \mathbb{P})$ to the SPDE for an SDSM on a bounded domain and the corresponding martingale problem for the SDSMs on a bounded domain is well-posed.

Citation

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Yan-Xia Ren. Renming Song. Hao Wang. "A class of stochastic partial differential equations for interacting superprocesses on a bounded domain." Osaka J. Math. 46 (2) 373 - 401, June 2009.

Information

Published: June 2009
First available in Project Euclid: 19 June 2009

zbMATH: 1170.60034
MathSciNet: MR2549592

Subjects:
Primary: 60G57, 60J80, 60K35
Secondary: 60G52

Rights: Copyright © 2009 Osaka University and Osaka City University, Departments of Mathematics

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Vol.46 • No. 2 • June 2009
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