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

Renming Song; Longjie Xie

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arXiv · 1804.05086

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

Renming Song·Longjie Xie

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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 the exponential ergodicity for the unique strong solution.

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BibTeX RIS

Renming Song, Longjie Xie. 2018-04-13. Well-posedness and long time behavior of singular Langevin stochastic differential equations. https://arxiv.org/abs/1804.05086

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