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

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  • Qingfeng Zhu
  • Yufeng Shi

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.

Suggested Citation

  • Qingfeng Zhu & Yufeng Shi, 2014. "Mean-Field Forward-Backward Doubly Stochastic Differential Equations and Related Nonlocal Stochastic Partial Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, March.
    • Handle: RePEc:hin:jnlaaa:194341
    DOI: 10.1155/2014/194341
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