Exponential Convergence in Entropy and Wasserstein Distance for McKean-Vlasov SDEs

2020/10/18 by Panpan Ren, Ren, Panpan, Feng‐Yu Wang +1 · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Geometric Analysis and Curvature Flows #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2010.08950

openalex publication_date 2020/10/18 · openalex created_date 2020/10/22 · openalex updated_date 2026/07/28

Abstract

The following type exponential convergence is proved for (non-degenerate or degenerate) McKean-Vlasov SDEs: W₂(μ_t,μ_∞)² +\rm Ent(μ_t|μ_∞)≤ c \rm e^-λt min\W₂(μ₀, μ_∞)²,\rm Ent(μ₀|μ_∞)\, t≥ 1, where c,λ>0 are constants, μ_t is the distribution of the solution at time t, μ_∞ is the unique invariant probability measure, \rm Ent is the relative entropy and W₂ is the L²-Wasserstein distance. In particular, this type exponential convergence holds for some (non-degenerate or degenerate) granular media type equations generalizing those studied in [CMV, GLW] on the exponential convergence in a mean field entropy.

Citations

• Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality
• Distribution dependent SDEs for Landau type equations
• Uniform Poincaré and logarithmic Sobolev inequalities for mean field particles systems
• McKean-Vlasov SDEs with Drifts Discontinuous under Wasserstein Distance

Cited by

• Exponential Ergodicity for Singular Reflecting McKean-Vlasov SDEs

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