Exponential Ergodicity for Singular Reflecting McKean-Vlasov SDEs
Probability
2023-03-10 v5
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.
Cite
@article{arxiv.2108.03908,
title = {Exponential Ergodicity for Singular Reflecting McKean-Vlasov SDEs},
author = {Feng-Yu Wang},
journal= {arXiv preprint arXiv:2108.03908},
year = {2023}
}
Comments
33 pages. arXiv admin note: text overlap with arXiv:2106.12737