Exponential Ergodicity in \W₁ for SDEs with Distribution Dependent Noise and Partially Dissipative Drifts

2024/11/21 by Xing Huang, Huang, Xing, Huaiqian Li +3 · 2 citations
Economics, Econometrics and Finance · #Economic theories and models #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2411.14090

openalex publication_date 2024/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Being concerned with ergodicity of McKean--Vlasov SDEs, we establish a general result on exponential ergodicity in the L¹-Wasserstein distance. The result is successfully applied to non-degenerate and multiplicative Brownian motion cases, degenerate second order systems, and even the additive α-stable noise, where the coefficients before the noise are allowed to be distribution dependent and the drifts are only assumed to be partially dissipative. Our results considerably improve existing ones whose coefficients before the noise are distribution-free.

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• Convergence rates for the p-Wasserstein distance of the empirical measures of an ergodic Markov process
• Ergodic distribution dependent BSDE and application to long-time behavior of finite horizon distribution dependent BSDE

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