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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (4): 517-526.doi: https://doi.org/10.1007/s10483-009-0412-x

• Articles • 上一篇    下一篇

Solutions to general forward-backward doubly stochastic differential equations

朱庆峰1，石玉峰2，宫献军2   

    1. School of Statistics and Mathematics, Shandong University of Finance,Jinan 250014,  P. R. China;
    2. School of Mathematics, Shandong University, Jinan 250100,  P. R. China
  • 收稿日期:2008-03-13 修回日期:2009-02-17 出版日期:2009-04-16 发布日期:2009-04-16

Solutions to general forward-backward doubly stochastic differential equations

 Qing-Feng ZHU1,Yu-Feng SHI2,Xian-Jun GONG2   

    1. School of Statistics and Mathematics, Shandong University of Finance,Jinan 250014,  P. R. China;
    2. School of Mathematics, Shandong University, Jinan 250100,  P. R. China
  • Received:2008-03-13 Revised:2009-02-17 Online:2009-04-16 Published:2009-04-16

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摘要： A general type of forward-backward doubly stochastic differential equations (FBDSDEs) is studied. It extends many important equations that have been well studied, including stochastic Hamiltonian systems. Under some much weaker monotonicity assumptions, the existence and uniqueness of measurable solutions are established with a method of continuation. Furthermore, the continuity and differentiability of the solutions to FBDSDEs depending on parameters is discussed.

关键词: forward-backward doubly stochastic differential equations; method of continuation,$H$-monotone

Abstract: A general type of forward-backward doubly stochastic differential equations (FBDSDEs) is studied. It extends many important equations that have been well studied, including stochastic Hamiltonian systems. Under some much weaker monotonicity assumptions, the existence and uniqueness of measurable solutions are established with a method of continuation. Furthermore, the continuity and differentiability of the solutions to FBDSDEs depending on parameters is discussed.

Key words: forward-backward doubly stochastic differential equations; method of continuation,$H$-monotone

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