Ergodicity for Time Changed Symmetric Stable Processes
نویسندگان
چکیده
In this paper we study the ergodicity and the related semigroup property for a class of symmetric Markov jump processes associated with time changed symmetric α-stable processes. For this purpose, explicit and sharp criteria for Poincaré type inequalities (including Poincaré, super Poincaré and weak Poincaré inequalities) of the corresponding non-local Dirichlet forms are derived. Moreover, our main results, when applied to a class of one-dimensional stochastic differential equations driven by symmetric α-stable processes, yield sharp criteria for their various ergodic properties and corresponding functional inequalities.
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