一般正倒向重随机微分方程的解

Solutions of General Forward-Backward Doubly Stochastic Differential Equations

研究了一类正倒向重随机微分方程,其涵盖了以前的包括随机Hamilton系统的很多情况.通过连续性方法,在较弱的单调条件下得到了其解的存在唯一性结果.然后研究了正倒向重随机微分方程的解依赖于参数的连续性和可微性.

A general type of forward-backward doubly stochastic differential equations （ FBDSDEs in short ） was studied, which extends many important equations well studied before, including stochastic Hamiltonian systems. Under some much weaker monotonicity assumptions, the existence and uniqueness results for measurable solutions were established by means of a method of continuation. Furthermore the continuity and differentiability of the solutions of FBDSDEs depending on parameters were discussed.