Two problems for stochastic flows associated with nonlinear parabolic equations

M. Nica, C. Vârsan

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)163-178
Number of pages16
JournalMathematical Reports
Volume18
Issue number2
Publication statusPublished - 2016
Externally publishedYes

Keywords

  • Fisk-Stratonovich stochastic integral
  • Gradient representation
  • Hamilton-Jacobi equations
  • Stochastic flow
  • Stochastic partial differential equation

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