Mean-Field Backward Doubly Stochastic Differential Equations and Applications
Probability
2011-08-30 v1
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.
Keywords
Cite
@article{arxiv.1108.5590,
title = {Mean-Field Backward Doubly Stochastic Differential Equations and Applications},
author = {Tianxiao Wang and Qingfeng Zhu and Yufeng Shi},
journal= {arXiv preprint arXiv:1108.5590},
year = {2011}
}