Exponential ergodicity for SDEs under the total variation

We establish a general criterion which ensures exponential ergodicity of Markov process on R d . 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 di...

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Bibliographic Details
Published inJournal of evolution equations Vol. 18; no. 3; pp. 1051 - 1067
Main Authors Peng, Xuhui, Zhang, Rangrang
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.09.2018
Springer Nature B.V
Subjects
Analysis
Criteria
Differential equations
Ergodic processes
Markov processes
Mathematics
Mathematics and Statistics
Ergodic
Coupling method
Exponential mixing
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Summary:We establish a general criterion which ensures exponential ergodicity of Markov process on R d . 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.
ISSN:1424-3199
1424-3202
DOI:10.1007/s00028-018-0429-3