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}
}
Comments
29 pages