Exponential Ergodicity for Singular Reflecting McKean-Vlasov SDEs
arXiv:2108.03908
Abstract
By refining a recent result of Xie and Zhang, we prove the exponential ergodicity under a weighted variation norm for singular SDEs with drift containing a local integrable term and a coercive term. This result is then extended to singular reflecting SDEs as well as singular McKean-Vlasov SDEs with or without reflection. We also present the exponential ergodicity in the relative entropy and (weighted) Wasserstein distances for reflecting McKean-Vlasov SDEs under the dissipative and partially dissipative conditions respectively. The main results are illustrated by non-symmetric singular granular media equations.
33 pages. arXiv admin note: text overlap with arXiv:2106.12737
References in corpus (4)
- A Zvonkin's transformation for stochastic differential equations with singular drift and related applications
- Distribution Dependent Reflecting Stochastic Differential Equations
- Exponential Convergence in Entropy and Wasserstein Distance for McKean-Vlasov SDEs
- Exponential Ergodicity for Non-Dissipative McKean-Vlasov SDEs