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Well-posedness and long time behavior of singular Langevin stochastic differential equations

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  • Song, Renming
  • Xie, Longjie

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.

Suggested Citation

  • Song, Renming & Xie, Longjie, 2020. "Well-posedness and long time behavior of singular Langevin stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1879-1896.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:4:p:1879-1896
    DOI: 10.1016/j.spa.2019.06.001
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    References listed on IDEAS

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    1. Wu, Liming, 2001. "Large and moderate deviations and exponential convergence for stochastic damping Hamiltonian systems," Stochastic Processes and their Applications, Elsevier, vol. 91(2), pages 205-238, February.
    2. Mattingly, J. C. & Stuart, A. M. & Higham, D. J., 2002. "Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise," Stochastic Processes and their Applications, Elsevier, vol. 101(2), pages 185-232, October.
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    Cited by:

    1. Xie, Longjie & Yang, Li, 2022. "The Smoluchowski–Kramers limits of stochastic differential equations with irregular coefficients," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 91-115.

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