Exponential ergodicity for singular reflecting McKean–Vlasov SDEs

By refining a recent result of Xie and Zhang (2020), 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 SDE...

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Bibliographic Details
Published inStochastic processes and their applications Vol. 160; pp. 265 - 293
Main Author Wang, Feng-Yu
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.06.2023
Subjects
Exponential ergodicity
Non-symmetric singular granular media equations
Reflecting McKean–Vlasov SDEs
Weighted variation norm
Exponential ergodicity
60H10
Reflecting McKean–Vlasov SDEs
Weighted variation norm
60G65
Non-symmetric singular granular media equations
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Summary:By refining a recent result of Xie and Zhang (2020), 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. The exponential ergodicity in the relative entropy and (weighted) Wasserstein distances are also studied for reflecting McKean–Vlasov SDEs. The main results are illustrated by non-symmetric singular granular media equations.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2023.03.009