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

Renming Song and Longjie Xie

Stochastic Processes and their Applications, 2020, vol. 130, issue 4, 1879-1896

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: Pathwise uniqueness; Langevin equation; Krylov’s estimate; Exponential ergodicity (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2019.06.001

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