Abstract
In this paper, we solve two problems for some nonlinear SPDE driven by Fisk-Stratonovich 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.
Original language | English |
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Pages (from-to) | 163-178 |
Number of pages | 16 |
Journal | Mathematical Reports |
Volume | 18 |
Issue number | 2 |
Publication status | Published - 2016 |
Externally published | Yes |
Keywords
- Fisk-Stratonovich stochastic integral
- Gradient representation
- Hamilton-Jacobi equations
- Stochastic flow
- Stochastic partial differential equation