Ergodicity for time-changed symmetric stable processes |
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Authors: | Zhen-Qing Chen Jian Wang |
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Affiliation: | 1. Department of Mathematics, University of Washington, Seattle, WA 98195, USA;2. School of Mathematics and Computer Science, Fujian Normal University, 350007, Fuzhou, PR China |
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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. |
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Keywords: | 60J75 60J25 60J27 |
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