The Link between Stochastic Differential Equations with Non-Markovian Coefficients and Backward Stoc

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In this paper, we conjecture and prove the link between stochastic differential equations with non-Markovian coefficients and nonlinear parabolic backward stochastic partial differential equa-tions, which is an extension of such kind of link in Markovian framework to non-Markovian framework. Different from Markovian framework, where the corresponding partial differential equation is determin-istic, the backward stochastic partial differential equation here has a pair of adapted solutions, and thus the link has a much different form. Moreover, two examples are given to demonstrate the applications of the derived link.
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