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Backward doubly stochastic differential equations with random coefficients and quasilinear stochastic PDEs. (arXiv:1810.06959v1 [math.PR])

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.查看全文

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