Two Problems for Stochastic Flows Associated with Nonlinear Parabolic Equations
نویسنده
چکیده
In this paper, we solve two problems for some nonlinear SPDE driven by FiskStratonovich stoachastic integral. The main assumption is the commuting property of the drift and diffusion vector fields with respect of the Lie bracket. In the first problem (P1) we construct a classical solution for some nonlinear SPDE of parabolic type by assuming the compatibilty condition concerning the mentioned vector fields. The second problem (P2) is a related filtering one for a non-markovian system of SDEs involving a backward parabolic equation of Kolmogorov type with parameter.
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