Ergodicity for time-changed symmetric stable processes

Zhen Qing Chen; Jian Wang

doi:10.1016/j.spa.2014.04.003

Ergodicity for time-changed symmetric stable processes

Zhen Qing Chen, Jian Wang^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

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.

Original language	English
Pages (from-to)	2799-2823
Number of pages	25
Journal	Stochastic Processes and their Applications
Volume	124
Issue number	9
DOIs	https://doi.org/10.1016/j.spa.2014.04.003
Publication status	Published - Sept 2014
Externally published	Yes

Keywords

Non-local Dirichlet forms
Poincaré type inequalities
Symmetric stable processes
Time change

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10.1016/j.spa.2014.04.003

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Chen, Z. Q., & Wang, J. (2014). Ergodicity for time-changed symmetric stable processes. Stochastic Processes and their Applications, 124(9), 2799-2823. https://doi.org/10.1016/j.spa.2014.04.003

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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 Poincar{\'e} type inequalities (including Poincar{\'e}, super Poincar{\'e} and weak Poincar{\'e} 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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AU - Wang, Jian

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AB - 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.

KW - Non-local Dirichlet forms

KW - Poincaré type inequalities

KW - Symmetric stable processes

KW - Time change

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JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 9

ER -

Ergodicity for time-changed symmetric stable processes

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Keywords

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