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, the 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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Bogachev, V., Da Prato, G. & Röckner, M. Existence and uniqueness of solutions for Fokker–Planck equations on Hilbert spaces. J. Evol. Equ. 10, 487–509 (2010). https://doi.org/10.1007/s00028-010-0058-y
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DOI: https://doi.org/10.1007/s00028-010-0058-y