Osaka Journal of Mathematics

A class of stochastic partial differential equations for interacting superprocesses on a bounded domain

Yan-Xia Ren, Renming Song, and Hao Wang

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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.

Article information

Source
Osaka J. Math., Volume 46, Number 2 (2009), 373-401.

Dates
First available in Project Euclid: 19 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1245415675

Mathematical Reviews number (MathSciNet)
MR2549592

Zentralblatt MATH identifier
1170.60034

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60G57: Random measures 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60G52: Stable processes

Citation

Ren, Yan-Xia; Song, Renming; Wang, Hao. A class of stochastic partial differential equations for interacting superprocesses on a bounded domain. Osaka J. Math. 46 (2009), no. 2, 373--401. https://projecteuclid.org/euclid.ojm/1245415675


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