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

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.

arXiv comment29 pages

Cited by in corpus (2)

• Strong uniqueness for SDEs in Hilbert spaces with nonregular drift
• A note on stochastic semilinear equations and their associated Fokker-Planck equations