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 the exponential ergodicity for the unique strong solution.

References in corpus (2)

• Ergodicity of stochastic differential equations with jumps and singular coefficients
• Couplings and quantitative contraction rates for Langevin dynamics