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Exponential ergodicity for SDEs and McKean-Vlasov processes with L\'{e}vy noise. (arXiv:1901.11125v1 [math.PR])
来源于:arXiv
We study stochastic differential equations (SDEs) of McKean-Vlasov type with
distribution dependent drifts and driven by pure jump L\'{e}vy processes. We
prove a uniform in time propagation of chaos result, providing quantitative
bounds on convergence rate of interacting particle systems with L\'{e}vy 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 L\'{e}vy-driven SDEs with distribution independent
coefficients. 查看全文>>