Exponential Ergodicity for Singular Reflecting McKean-Vlasov SDEs

2021/08/09 by Wang, Feng-Yu · 2 citations
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/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.

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