Exponential ergodicity for SDEs and McKean-Vlasov processes with Lévy noise

Mingjie Liang, Mateusz B. Majka, Jian Wang

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1 Citation (Scopus)
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Abstract

We study exponential ergodicity of a broad class of stochastic processes whose dynamics are governed by pure jump Lévy noise. In the first part of the paper we focus on solutions of stochastic differential equations (SDEs) whose drifts satisfy general Lyapunov-type conditions. By applying techniques that combine couplings, appropriately constructed L1-Wasserstein distances and Lyapunov functions, we show exponential convergence of solutions of such SDEs to their stationary distributions, both in the total variation and Wasserstein distances. The second part of the paper is devoted to SDEs of McKean–Vlasov type with distribution dependent drifts. We prove a uniform in time propagation of chaos result, providing quantitative bounds on convergence rate of interacting particle systems with Lévy noise to the corresponding McKean–Vlasov SDE. Then, extending our techniques from the first part of the paper, we obtain results on exponential ergodicity of solutions of McKean–Vlasov SDEs, under general conditions on the drift and the driving noise.
Original languageEnglish
Pages (from-to)1665-1701
Number of pages37
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume57
Issue number3
Early online date22 Jul 2021
DOIs
Publication statusPublished - Aug 2021

Keywords

  • Coupling
  • Exponential ergodicity
  • Lévy noise
  • McKean–Vlasov process
  • Mean-field SDE
  • Propagation of chaos

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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