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Well-posedness and long time behavior of singular Langevin stochastic differential equations. (English) Zbl 1457.60102

Summary: 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.

MSC:

60H17 Singular stochastic partial differential equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
37A25 Ergodicity, mixing, rates of mixing
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
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