Well-posedness and long time behavior of singular Langevin stochastic differential equations
Probability
2018-09-06 v2 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.1804.05086,
title = {Well-posedness and long time behavior of singular Langevin stochastic differential equations},
author = {Renming Song and Longjie Xie},
journal= {arXiv preprint arXiv:1804.05086},
year = {2018}
}