Well-posedness and long time behavior of singular Langevin stochastic differential equations |
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| Affiliation: | 1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA;2. LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China;3. School of Mathematical Science, University of Chinese Academy of Sciences, Beijing, 100049, China;1. University of Chicago, United States of America;2. University of Oxford, UK;3. NYU Shanghai, China;1. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Building 27, 1 Gwanak-ro, Gwanak-gu Seoul, 08826, Republic of Korea;2. Department of Mathematical Sciences, Seoul National University, Building 27, 1 Gwanak-ro, Gwanak-gu Seoul 08826, Republic of Korea |
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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 exponential ergodicity for the unique strong solution. |
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| Keywords: | Pathwise uniqueness Langevin equation Krylov’s estimate Exponential ergodicity |
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