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

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

2009-07-09

arxiv.org/abs/0907.1431v1

Mathematics

Probability

29 pages

Scientific paper

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.

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