Exponential ergodicity for SDEs under the total variation

Xuhui Peng; Rangrang Zhang

doi:10.1007/s00028-018-0429-3

Exponential ergodicity for SDEs under the total variation

Xuhui Peng
, Rangrang Zhang^*

^*Corresponding author for this work

School of Mathematics and Statistics

Hunan Normal University

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

4 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1051-1067
Number of pages	17
Journal	Journal of Evolution Equations
Volume	18
Issue number	3
DOIs	https://doi.org/10.1007/s00028-018-0429-3
Publication status	Published - 1 Sept 2018

Keywords

Coupling method
Ergodic
Exponential mixing

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10.1007/s00028-018-0429-3

Cite this

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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{\textendash}2091, 2008). Applying our criterion to stochastic differential equations driven by L{\'e}vy noise, we obtain the exponential ergodicity. Our noise can be more degenerate than the existing results.",

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AB - 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.

KW - Coupling method

KW - Ergodic

KW - Exponential mixing

UR - https://www.scopus.com/pages/publications/85044966678

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ER -

Exponential ergodicity for SDEs under the total variation

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Keywords

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