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

Abstract

We study stochastic differential equations (SDEs) of McKean-Vlasov type with distribution dependent drifts and driven by pure jump Lévy processes. 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. By applying techniques that combine couplings, appropriately constructed $L^1$-Wasserstein distances and Lyapunov functions, we show exponential convergence of solutions of such SDEs to their stationary distributions. Our methods allow us to obtain results that are novel even for a broad class of Lévy-driven SDEs with distribution independent coefficients.

arXiv comment44 pages

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• Coupling approach for exponential ergodicity of stochastic Hamiltonian systems with Lévy noises