Forward-backward doubly stochastic systems and classical solutions of path-dependent stochastic PDEs

Yufeng Shi; Jiaqiang Wen; Jie Xiong

doi:10.1080/17442508.2022.2085503

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arXiv · 2206.05435

Forward-backward doubly stochastic systems and classical solutions of path-dependent stochastic PDEs

Yufeng Shi·Jiaqiang Wen·Jie Xiong

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Abstract

In this paper, a class of non-Markovian forward-backward doubly stochastic systems is studied. By using the technique of functional It\^o (or path-dependent) calculus, the relationship between the systems and related path-dependent quasi-linear stochastic partial differential equations (SPDEs in short) is established, and the well-known nonlinear stochastic Feynman-Kac formula of Pardoux and Peng [Backward doubly stochastic differential equations and systems of quasilinear SPDEs, Probab. Theory Relat. Fields 98 (1994), pp. 209--227] is developed to the non-Markovian situation. Moreover, we obtain the differentiability of the solution to the forward-backward doubly stochastic systems and some properties of solutions to the path-dependent SPDEs.

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Yufeng Shi, Jiaqiang Wen, Jie Xiong. 2022-06-11. Forward-backward doubly stochastic systems and classical solutions of path-dependent stochastic PDEs. https://doi.org/10.1080/17442508.2022.2085503

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