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Exponential Ergodicity for Singular McKean–Vlasov Stochastic Differential Equations in Weighted Variation Metric

Author

Listed:
  • Shanshan Hu

    (Tianjin University)

  • Yue Wang

    (Shenzhen Polytechnic University)

Abstract

In this paper, we prove exponential ergodicity for McKean–Vlasov stochastic differential equations (SDEs) with singular drift under a weighted variation metric. The McKean–Vlasov SDE is perturbed by a singular potential and does not completely satisfy the typical dissipative condition in the x-variable. Our conclusion extends some ergodicity results in total variation norm with or without dependence on distribution and indicates ergodicity under Wasserstein distance if the weight function is chosen in a particular way. Furthermore, we apply the main result to nonlinear Fokker–Planck equations, in particular, to non-symmetric singular granular media equations, and observe the long-time behavior of the SDEs.

Suggested Citation

  • Shanshan Hu & Yue Wang, 2025. "Exponential Ergodicity for Singular McKean–Vlasov Stochastic Differential Equations in Weighted Variation Metric," Journal of Theoretical Probability, Springer, vol. 38(1), pages 1-34, March.
    • Handle: RePEc:spr:jotpro:v:38:y:2025:i:1:d:10.1007_s10959-024-01398-2
    DOI: 10.1007/s10959-024-01398-2
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