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Singular McKean-Vlasov (reflecting) SDEs with distribution dependent noise

Xing Huang, Feng-yu Wang

Journal of Mathematical Analysis and Applications, Volume: 514, Issue: 1, Start page: 126301

Swansea University Author: Feng-yu Wang

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DOI (Published version): 10.1016/j.jmaa.2022.126301

Abstract

By using Zvonkin's transformation and a two-step fixed point argument in distributions, the well-posedness and regularity estimates are derived for singular McKean-Vlasov SDEs with distribution dependent noise, where the drift contains a term growing linearly in space and distribution and a loc...

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Published in: Journal of Mathematical Analysis and Applications
ISSN: 0022-247X
Published: Elsevier BV 2022
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa59935
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Abstract: By using Zvonkin's transformation and a two-step fixed point argument in distributions, the well-posedness and regularity estimates are derived for singular McKean-Vlasov SDEs with distribution dependent noise, where the drift contains a term growing linearly in space and distribution and a locally integrable term independent of distribution, while the noise coefficient is weakly differentiable in space and Lipschitz continuous in distribution with respect to the sum of Wasserstein and weighted variation distances. The main results extend existing ones derived for noise coefficients either independent of distribution, or having nice linear functional derivatives in distribution. Singular reflecting SDEs with distribution dependent noise are also studied.
Keywords: McKean-Vlasov SDEs; Wasserstein distance; Two-step fixed point argument; Weighted variation distance
College: Faculty of Science and Engineering
Issue: 1
Start Page: 126301

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