Abstract and Applied Analysis

Mean-Field Forward-Backward Doubly Stochastic Differential Equations and Related Nonlocal Stochastic Partial Differential Equations

Qingfeng Zhu and Yufeng Shi

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 194341, 10 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412606753

Digital Object Identifier
doi:10.1155/2014/194341

Mathematical Reviews number (MathSciNet)
MR3191023

Zentralblatt MATH identifier
07021911

Citation

Zhu, Qingfeng; Shi, Yufeng. Mean-Field Forward-Backward Doubly Stochastic Differential Equations and Related Nonlocal Stochastic Partial Differential Equations. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 194341, 10 pages. doi:10.1155/2014/194341. https://projecteuclid.org/euclid.aaa/1412606753


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