Backward doubly stochastic differential equations with random coefficients and quasilinear stochastic PDEs

Jiaqiang Wen; Yufeng Shi

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arXiv · 1810.06959

Backward doubly stochastic differential equations with random coefficients and quasilinear stochastic PDEs

Jiaqiang Wen·Yufeng Shi

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Abstract

In this paper, by virtue of Malliavin calculus, we establish a relationship between backward doubly stochastic differential equations with random coefficients and quasilinear stochastic PDEs, and thus extend the well-known nonlinear stochastic Feynman-Kac formula of Pardoux and Peng [14] to non-Markovian case.

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Jiaqiang Wen, Yufeng Shi. 2018-10-16. Backward doubly stochastic differential equations with random coefficients and quasilinear stochastic PDEs. https://arxiv.org/abs/1810.06959

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