Well-posedness and long time behavior of singular Langevin stochastic differential equations

Renming Song; Longjie Xie

doi:10.1016/j.spa.2019.06.001

Well-posedness and long time behavior of singular Langevin stochastic differential equations

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

Abstract

In this paper, we study damped Langevin stochastic differential equations with singular velocity fields. We prove the strong well-posedness of such equations. Moreover, by combining the technique of Lyapunov functions with Krylov's estimate, we also establish exponential ergodicity for the unique strong solution.

Original language	English (US)
Pages (from-to)	1879-1896
Number of pages	18
Journal	Stochastic Processes and their Applications
Volume	130
Issue number	4
DOIs	https://doi.org/10.1016/j.spa.2019.06.001
State	Published - Apr 2020

Keywords

Exponential ergodicity
Krylov's estimate
Langevin equation
Pathwise uniqueness

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

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10.1016/j.spa.2019.06.001

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title = "Well-posedness and long time behavior of singular Langevin stochastic differential equations",

abstract = "In this paper, we study damped Langevin stochastic differential equations with singular velocity fields. We prove the strong well-posedness of such equations. Moreover, by combining the technique of Lyapunov functions with Krylov's estimate, we also establish exponential ergodicity for the unique strong solution.",

keywords = "Exponential ergodicity, Krylov's estimate, Langevin equation, Pathwise uniqueness",

author = "Renming Song and Longjie Xie",

note = "Funding Information: Research of R. Song is supported by the Simons Foundation (# 429343 , Renming Song). L. Xie is supported by the Alexander von Humboldt Stiftung Foundation, Germany , NNSF of China (No. 11701233 ) and Natural Science Foundation of Jiangsu Province (No. BK20170226 ). The Project Funded by the PAPD of Jiangsu Higher Education Institutions is also gratefully acknowledged. Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",

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AU - Xie, Longjie

N1 - Funding Information: Research of R. Song is supported by the Simons Foundation (# 429343 , Renming Song). L. Xie is supported by the Alexander von Humboldt Stiftung Foundation, Germany , NNSF of China (No. 11701233 ) and Natural Science Foundation of Jiangsu Province (No. BK20170226 ). The Project Funded by the PAPD of Jiangsu Higher Education Institutions is also gratefully acknowledged. Publisher Copyright: © 2019 Elsevier B.V.

PY - 2020/4

Y1 - 2020/4

N2 - In this paper, we study damped Langevin stochastic differential equations with singular velocity fields. We prove the strong well-posedness of such equations. Moreover, by combining the technique of Lyapunov functions with Krylov's estimate, we also establish exponential ergodicity for the unique strong solution.

AB - In this paper, we study damped Langevin stochastic differential equations with singular velocity fields. We prove the strong well-posedness of such equations. Moreover, by combining the technique of Lyapunov functions with Krylov's estimate, we also establish exponential ergodicity for the unique strong solution.

KW - Exponential ergodicity

KW - Krylov's estimate

KW - Langevin equation

KW - Pathwise uniqueness

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Well-posedness and long time behavior of singular Langevin stochastic differential equations

Abstract

Keywords

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