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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, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:194341
    DOI: 10.1155/2014/194341
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    References listed on IDEAS

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    1. V. Bally & A. Matoussi, 2001. "Weak Solutions for SPDEs and Backward Doubly Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 14(1), pages 125-164, January.
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