Mean-Field Backward Doubly Stochastic Differential Equations and Applications

Details Mean-Field Backward Doubly Stochastic Differential Equations and Applications Mean-Field Backward Doubly Stochastic Differential Equations and Applications

2011-08-29

arxiv.org/abs/1108.5590v1

Mathematics

Probability

Scientific paper

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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