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Zhu, Qingfeng; Shi, Yufeng

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

Abstr. Appl. Anal. 2014, Article ID 194341, 10 p. (2014).
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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References:

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