Mean-Field Backward Doubly Stochastic Differential Equations and Applications

2011/08/29 by Wang, Tianxiao, Zhu, Qingfeng, Shi, Yufeng
#60H05 #60H15 #93E20 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1108.5590

Abstract

Mean-field backward doubly stochastic differential equations (MF-BDSDEs, for short) are introduced and studied. The existence and uniqueness of solutions for MF-BDSDEs is established. One probabilistic interpretation for the solutions to a class of nonlocal stochastic partial differential equations (SPDEs, for short) is given. A Pontryagin's type maximum principle is established for optimal control problem of MF-BDSDEs. Finally, one backward linear quadratic problem of mean-field type is discussed to illustrate the direct application of above maximum principle.

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