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**Mean-field forward-backward doubly stochastic differential equations and related nonlocal stochastic partial differential equations.**
*(English)*
Zbl 1469.60200

Summary: Mean-field forward-backward doubly stochastic differential equations (MF-FBDSDEs) are studied, which extend many important equations well studied before. Under some suitable monotonicity assumptions, the existence and uniqueness results for measurable solutions are established by means of a method of continuation. Furthermore, the probabilistic interpretation for the solutions to a class of nonlocal stochastic partial differential equations (SPDEs) combined with algebra equations is given.

### MSC:

60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |

60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |

### Keywords:

nonlocal stochastic partial differential equations; mean-field forward-backward doubly stochastic differential equations
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\textit{Q. Zhu} and \textit{Y. Shi}, Abstr. Appl. Anal. 2014, Article ID 194341, 10 p. (2014; Zbl 1469.60200)

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