Anticipated backward doubly stochastic differential equations

Xiaoming Xu

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arXiv · 1207.6165

Anticipated backward doubly stochastic differential equations

Xiaoming Xu

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Abstract

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).

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Xiaoming Xu. 2013-07-09. Anticipated backward doubly stochastic differential equations. https://arxiv.org/abs/1207.6165

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