Uniqueness of Invariant Measures of Infinite Dimensional Stochastic Differential Equations Driven by L,vy Noises

作者：Xie Bin^*

来源：Potential Analysis, 2012, 36(1): 35-66.

DOI：10.1007/s11118-011-9220-6

• Invariant measure
• Levy noise
• Bismut-Elworthy-Li formula
• Strong Feller
• Irreducibility
• Uniqueness

In this paper, we are attempting to study the uniqueness of invariant measures of a stochastic differential equation driven by a L,vy 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.

• 出版日期2012-1