Mean-field backward doubly stochastic differential equations and related SPDEs

被引：12
|
作者：
Xu, Ruimin [1 ,2 ]
机构：
[1] Shandong Univ, Sch Math, Jinan 250100, Peoples R China
[2] Shandong Polytech Univ, Sch Math, Jinan 250353, Peoples R China
来源：
BOUNDARY VALUE PROBLEMS | 2012年
关键词：
mean-field; backward doubly stochastic differential equations; locally monotone coefficients; comparison theorem; stochastic partial differential equations; PARTICLE METHOD; MCKEAN-VLASOV; COEFFICIENTS; SYSTEMS; BDSDES;
D O I：
10.1186/1687-2770-2012-114
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Existence and uniqueness result of the solutions to mean-field backward doubly stochastic differential equations (BDSDEs in short) with locally monotone coefficients as well as the comparison theorem for these equations are established. As a preliminary step, the existence and uniqueness result for the solutions of mean-field BDSDEs with globally monotone coefficients is also established. Furthermore, we give the probabilistic representation of the solutions for a class of stochastic partial differential equations by virtue of mean-field BDSDEs, which can be viewed as the stochastic Feynman-Kac formula for SPDEs of mean-field type.
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页数：20
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