English

Existence and uniqueness of solutions for Fokker-Planck equations on Hilbert spaces

Probability 2018-06-18 v1

Abstract

We consider a stochastic differential equation in a Hilbert space with time-dependent coefficients for which no general existence and uniqueness results are known. We prove, under suitable assumptions, existence and uniqueness of a measure valued solution, for the corresponding Fokker--Planck equation. In particular, we verify the Chapman--Kolmogorov equations and get an evolution system of transition probabilities for the stochastic dynamics informally given by the stochastic differential equation.

Keywords

Cite

@article{arxiv.0907.1431,
  title  = {Existence and uniqueness of solutions for Fokker-Planck equations on Hilbert spaces},
  author = {Vladimir Bogachev and Giuseppe Da Prato and Michael Röckner},
  journal= {arXiv preprint arXiv:0907.1431},
  year   = {2018}
}

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29 pages