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Backward doubly stochastic differential equations with random coefficients and quasilinear stochastic PDEs (1810.06959v1)
Published 16 Oct 2018 in math.PR
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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