Approximate McKean-Vlasov representations for a class of SPDEs

被引：62

作者：

Crisan, Dan ^{[1
]}

Xiong, Jie ^{[2
,3
]}

机构：

[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2BZ, England

[2] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

[3] Hebei Normal Univ, Dept Math, Shijiazhuang 050016, Peoples R China

来源：

STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES | 2010年 / 82卷 / 01期

关键词：

stochastic partial differential equations; particle approximations; McKean-Vlasov equations; Zakai equation; Kushner-Stratonovitch equation; non-linear diffusions; PARTICLE APPROXIMATION; CONVERGENCE;

D O I：

10.1080/17442500902723575

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The solution (sic) = ((sic)(t))(t >= 0) 0 of a class of linear stochastic partial differential equations is approximated using Clark's robust representation approach. The ensuing approximations are shown to coincide with the time marginals of solutions of a certain McKean-Vlasov type equation. We prove existence and uniqueness of the solution of the McKean-Vlasov equation.

引用

页码：53 / 68

页数：16

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