Exponential ergodicity for SDEs under the total variation

Xuhui Peng, Rangrang Zhang*

*Corresponding author for this work

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Abstract

We establish a general criterion which ensures exponential ergodicity of Markov process on Rd. Compared with the classical irreducible condition, we only require a weak form of irreducibility given by Hairer and Mattingly (Ann Probab 36(6):2050–2091, 2008). Applying our criterion to stochastic differential equations driven by Lévy noise, we obtain the exponential ergodicity. Our noise can be more degenerate than the existing results.

Original languageEnglish
Pages (from-to)1051-1067
Number of pages17
JournalJournal of Evolution Equations
Volume18
Issue number3
DOIs
Publication statusPublished - 1 Sept 2018

Keywords

  • Coupling method
  • Ergodic
  • Exponential mixing

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Peng, X., & Zhang, R. (2018). Exponential ergodicity for SDEs under the total variation. Journal of Evolution Equations, 18(3), 1051-1067. https://doi.org/10.1007/s00028-018-0429-3