The Uniqueness Of Invariant Measures Of Stable Processes And Operator-stable Processes

The uniqueness of invariant measures is a very important problem in the theory of Markov processes. In this paper, we generalize the conclusion that symmetric stable processes all have unique invariant measures to some large class of stable processes which includes all symmetric stable processes. Moreover, we obtain the result that all operator-stable processes have unique invariant measures under a certain conditions.