Anticipated backward doubly stochastic differential equations
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摘要
In this paper, we deal with a new type of differential equations called anticipated backward doubly stochastic differential equations (anticipated BDSDEs). The coefficients of these BDSDEs depend on the future value of the solution (Y,Z). We obtain the existence and uniqueness theorem and a comparison theorem for the solutions of these equations. Besides, as an application, we also establish a duality between the anticipated BDSDEs and the delayed doubly stochastic differential equations (delayed DSDEs).
论文关键词:Anticipated backward doubly stochastic differential equation,Comparison theorem,Duality
论文评审过程:Available online 3 July 2013.
论文官网地址:https://doi.org/10.1016/j.amc.2013.05.054