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Journal of Statistical Physics

, Volume 154, Issue 4, pp 929–949 | Cite as

Exponential Ergodicity of Stochastic Burgers Equations Driven by α-Stable Processes

  • Zhao Dong
  • Lihu Xu
  • Xicheng Zhang
Article

Abstract

In this work, we prove the strong Feller property and the exponential ergodicity of stochastic Burgers equations driven by α/2-subordinated cylindrical Brownian motions with α∈(1,2). To prove the results, we truncate the nonlinearity and use the derivative formula for SDEs driven by α-stable noises established in (Zhang in Stoch. Process. Appl. 123(4):1213–1228, 2013).

Keywords

Alpha-stable processes Burgers equations Exponential mixing 

Notes

Acknowledgements

We would like to thank Vahagn Nersesyan for stimulating discussions on exponential mixing. Special thanks are due to the referee for carefully reviewing the paper and giving many useful suggestions. Zhao Dong is supported by ‘Key Laboratory of Random Complex Structures and Data Sciences, AMSS, CAS’ (No. 2008DP173182), ‘Science Fund for Creative Research Groups (10721101)’, 973 Program (2011CB808000), NSFC (Nos. 11271356, 11371041). Xicheng Zhang is supported by NSFs of China (No. 11271294) and Program for New Century Excellent Talents in University.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institute of Applied Mathematics, AMSSCASBeijingP.R. China
  2. 2.Department of MathematicsBrunel UniversityUxbridgeUK
  3. 3.Department of Mathematics, Faculty of Science and TechnologyUniversity of MacauTaipaP.R. China
  4. 4.School of Mathematics and StatisticsWuhan UniversityWuhanP.R. China

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