We prove existence and, under an additional assumption, uniqueness of an evolution system of measures for a stochastic differential equation with time dependent dissipative coefficients. We prove that if denotes the corresponding transition evolution operator, then behaves asymptotically as like a limit curve (which is independent of ) for any continuous and bounded ``observable'' .
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Michael Röckner, Giuseppe Da Prato, Dissipative stochastic equations in Hilbert space with time dependent coefficients. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 17 (2006), no. 4, pp. 397–403DOI 10.4171/RLM/476