Exponential ergodicity of non-Lipschitz multivalued stochastic differential equations

Jiagang Ren; Jing Wu; Xicheng Zhang

doi:10.1016/j.bulsci.2009.01.003

Exponential ergodicity of non-Lipschitz multivalued stochastic differential equations

Jiagang Ren^*, Jing Wu, Xicheng Zhang

^*Corresponding author for this work

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

31 Citations (Scopus)

Abstract

Under the conditions of coefficients being non-Lipschitz and the diffusion coefficient being elliptic, we study the strong Feller property and irreducibility for the transition probability of solutions to general multivalued stochastic differential equations by using the coupling method, Girsanov's theorem and a stopping argument. Thus we can establish the exponential ergodicity and the spectral gap.

Original language	English
Pages (from-to)	391-404
Number of pages	14
Journal	Bulletin des Sciences Mathematiques
Volume	134
Issue number	4
DOIs	https://doi.org/10.1016/j.bulsci.2009.01.003
Publication status	Published - Jun 2010
Externally published	Yes

Keywords

Ellipticity
Ergodicity
Girsanov's theorem
Irreducibility
Non-Lipschitz multivalued stochastic differential equation
Stopping time
Strong Feller property

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10.1016/j.bulsci.2009.01.003

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abstract = "Under the conditions of coefficients being non-Lipschitz and the diffusion coefficient being elliptic, we study the strong Feller property and irreducibility for the transition probability of solutions to general multivalued stochastic differential equations by using the coupling method, Girsanov's theorem and a stopping argument. Thus we can establish the exponential ergodicity and the spectral gap.",

keywords = "Ellipticity, Ergodicity, Girsanov's theorem, Irreducibility, Non-Lipschitz multivalued stochastic differential equation, Stopping time, Strong Feller property",

author = "Jiagang Ren and Jing Wu and Xicheng Zhang",

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T1 - Exponential ergodicity of non-Lipschitz multivalued stochastic differential equations

AU - Ren, Jiagang

AU - Wu, Jing

AU - Zhang, Xicheng

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N2 - Under the conditions of coefficients being non-Lipschitz and the diffusion coefficient being elliptic, we study the strong Feller property and irreducibility for the transition probability of solutions to general multivalued stochastic differential equations by using the coupling method, Girsanov's theorem and a stopping argument. Thus we can establish the exponential ergodicity and the spectral gap.

AB - Under the conditions of coefficients being non-Lipschitz and the diffusion coefficient being elliptic, we study the strong Feller property and irreducibility for the transition probability of solutions to general multivalued stochastic differential equations by using the coupling method, Girsanov's theorem and a stopping argument. Thus we can establish the exponential ergodicity and the spectral gap.

KW - Ellipticity

KW - Ergodicity

KW - Girsanov's theorem

KW - Irreducibility

KW - Non-Lipschitz multivalued stochastic differential equation

KW - Stopping time

KW - Strong Feller property

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DO - 10.1016/j.bulsci.2009.01.003

M3 - Article

AN - SCOPUS:77953138971

SN - 0007-4497

VL - 134

SP - 391

EP - 404

JO - Bulletin des Sciences Mathematiques

JF - Bulletin des Sciences Mathematiques

IS - 4

ER -

Exponential ergodicity of non-Lipschitz multivalued stochastic differential equations

Abstract

Keywords

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