Exponential ergodicity of non-Lipschitz stochastic differential equations

Xicheng Zhang

doi:10.1090/S0002-9939-08-09509-9

Exponential ergodicity of non-Lipschitz stochastic differential equations

Xicheng Zhang^*

^*Corresponding author for this work

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

22 Citations (Scopus)

Abstract

Using the coupling method and Girsanov's theorem, we study the strong Feller property and irreducibility for the transition probabilities of stochastic differential equations with non-Lipschitz and monotone coefficients. Then, the exponential ergodicity and the spectral gap for the corresponding transition semigroups are obtained under fewer assumptions.

Original language	English
Pages (from-to)	329-337
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	137
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-08-09509-9
Publication status	Published - Jan 2009
Externally published	Yes

Keywords

Ergodicity
Irreducibility
Non-Lipschitz stochastic differential equation
Spectral gap
Strong Feller property

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10.1090/S0002-9939-08-09509-9

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abstract = "Using the coupling method and Girsanov's theorem, we study the strong Feller property and irreducibility for the transition probabilities of stochastic differential equations with non-Lipschitz and monotone coefficients. Then, the exponential ergodicity and the spectral gap for the corresponding transition semigroups are obtained under fewer assumptions.",

keywords = "Ergodicity, Irreducibility, Non-Lipschitz stochastic differential equation, Spectral gap, Strong Feller property",

author = "Xicheng Zhang",

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AB - Using the coupling method and Girsanov's theorem, we study the strong Feller property and irreducibility for the transition probabilities of stochastic differential equations with non-Lipschitz and monotone coefficients. Then, the exponential ergodicity and the spectral gap for the corresponding transition semigroups are obtained under fewer assumptions.

KW - Ergodicity

KW - Irreducibility

KW - Non-Lipschitz stochastic differential equation

KW - Spectral gap

KW - Strong Feller property

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Exponential ergodicity of non-Lipschitz stochastic differential equations

Abstract

Keywords

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