A class of stochastic partial differential equations for interacting superprocesses on a bounded domain
Ren, Yan-Xia ; Song, Renming ; Wang, Hao
Osaka J. Math., Tome 46 (2009) no. 1, p. 373-401 / Harvested from Project Euclid
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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.
Publié le : 2009-06-15
Classification:  60J80,  60G57,  60K35,  60G52 
@article{1245415675,
     author = {Ren, Yan-Xia and Song, Renming and Wang, Hao},
     title = {A class of stochastic partial differential equations for interacting superprocesses on a bounded domain},
     journal = {Osaka J. Math.},
     volume = {46},
     number = {1},
     year = {2009},
     pages = { 373-401},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1245415675}
}

Ren, Yan-Xia; Song, Renming; Wang, Hao. A class of stochastic partial differential equations for interacting superprocesses on a bounded domain. Osaka J. Math., Tome 46 (2009) no. 1, pp.  373-401. http://gdmltest.u-ga.fr/item/1245415675/