Uniqueness of Invariant Measures of Infinite Dimensional Stochastic Differential Equations Driven by Lévy Noises

Abstract

In this paper, we are attempting to study the uniqueness of invariant measures of a stochastic differential equation driven by a Levy type noise in a real separable Hilbert space. To investigate this problem, we study the strong Feller property and irreducibility of the corresponding Markov transition semigroup respectively. To show the strong Feller property, we generalize a Bismut–Elworthy–Li type formula to our Markov transition semigroup under a non-degeneracy condition of the coefficient of the Wiener process.