Well-posedness and long time behavior of singular Langevin stochastic differential equations
classification
🧮 math.PR
math.DS
keywords
equationsdifferentiallangevinsingularstochasticstrongwell-posednessbehavior
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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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