Log-Sobolev inequalities and exponential ergodicity for non-degenerate and degenerate McKean-Vlasov SDEs
Abstract
The exponential ergodicity of partially dissipative McKean-Vlasov SDEs in the L 1 -Wasserstein distance has been extensively studied using asymptotic reflection coupling. However, the reflection coupling method is not applicable for the exponential ergodicity in L 2 -Wasserstein distance and relative entropy. In this paper, we first establish uniform log-Sobolev inequalities (in the frozen measure variable with bounded second moments) for the invariant probability measure of the corresponding SDEs with frozen distribution. Second, for the McKean-Vlasov SDEs, we combine the log-Harnack inequality and Talagrand's inequality to derive exponential ergodicity in both L 2 -Wasserstein distance and relative entropy. Furthermore, we extend these main results to the case of degenerate diffusion.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Stochastic processes and financial applications
Statistical Mechanics and Entropy
Publication details
- Journal / source
- Journal of Functional Analysis
- Publisher
- Elsevier BV
- Volume
- 290
- Issue
- 10
- Pages
- 111410–111410
- Publication date
- 10 February 2026
- Language
- EN