Uniqueness of invariant measures of infinite dimensional stochastic differential equations driven by Lévy noises
The author investigates uniqueness of invariant measures for stochastic differential equation driven by a Lévy type noise in a real separable Hilbert space. A non-degeneracy condition on the coefficient of the Wiener process is assumed. Uniqueness of invariant measures is established by proving both strong Feller property and irreducibility of the corresponding Markov transition semigroup. In particular, the strong Feller property is based on a Bismut-Elworthy-Li type formula in infinite dimensions. A related Bismut-Elworthy-Li type formula has been recently proved by \textit{C. Marinelli, C. Prévôt} and \textit{M. Röckner} [J. Funct. Anal. 258, No. 2, 616--649 (2010; Zbl 1186.60060)].
scientific article; zbMATH DE number 5996884
scientific article