Ergodicity for time-changed symmetric stable processes

Zhen-Qing Chen and Jian Wang

Stochastic Processes and their Applications, 2014, vol. 124, issue 9, 2799-2823

Abstract: In this paper we study ergodicity and 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.

Keywords: Symmetric stable processes; Time change; Poincaré type inequalities; Non-local Dirichlet forms (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (6)

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DOI: 10.1016/j.spa.2014.04.003

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