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.
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页码：53 / 68
页数：16
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