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Exponential ergodicity of non-Lipschitz stochastic differential equations

Author: Xicheng Zhang
Journal: Proc. Amer. Math. Soc. 137 (2009), 329-337
MSC (2000): Primary 60H10, 37A25
Published electronically: May 15, 2008
MathSciNet review: 2439457
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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.

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Xicheng Zhang
Affiliation: Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, People’s Republic of China
Address at time of publication: School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW 2052, Australia

Keywords: Strong Feller property, irreducibility, ergodicity, spectral gap, non-Lipschitz stochastic differential equation.
Received by editor(s): August 6, 2007
Received by editor(s) in revised form: December 15, 2007
Published electronically: May 15, 2008
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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