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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
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URI: https://cronfa.swan.ac.uk/Record/cronfa59935
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first_indexed 2022-05-27T09:36:13Z
last_indexed 2022-05-28T03:35:19Z
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spelling v2 59935 2022-05-02 Singular McKean-Vlasov (reflecting) SDEs with distribution dependent noise 6734caa6d9a388bd3bd8eb0a1131d0de Feng-yu Wang Feng-yu Wang true false 2022-05-02 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. Journal Article Journal of Mathematical Analysis and Applications 514 1 126301 Elsevier BV 0022-247X McKean-Vlasov SDEs; Wasserstein distance; Two-step fixed point argument; Weighted variation distance 1 10 2022 2022-10-01 10.1016/j.jmaa.2022.126301 COLLEGE NANME COLLEGE CODE Swansea University Not Required 2024-07-10T12:21:12.2002538 2022-05-02T08:30:39.4487947 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Xing Huang 1 Feng-yu Wang 2 59935__23953__570840191e5e4cefb1148765cfd255e6.pdf 21HWc.pdf 2022-05-02T08:33:22.5932296 Output 319132 application/pdf Accepted Manuscript true 2023-05-04T00:00:00.0000000 ©2022 All rights reserved. All article content, except where otherwise noted, is licensed under a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND) true eng https://creativecommons.org/licenses/by-nc-nd/4.0/
title Singular McKean-Vlasov (reflecting) SDEs with distribution dependent noise
spellingShingle Singular McKean-Vlasov (reflecting) SDEs with distribution dependent noise
Feng-yu Wang
title_short Singular McKean-Vlasov (reflecting) SDEs with distribution dependent noise
title_full Singular McKean-Vlasov (reflecting) SDEs with distribution dependent noise
title_fullStr Singular McKean-Vlasov (reflecting) SDEs with distribution dependent noise
title_full_unstemmed Singular McKean-Vlasov (reflecting) SDEs with distribution dependent noise
title_sort Singular McKean-Vlasov (reflecting) SDEs with distribution dependent noise
author_id_str_mv 6734caa6d9a388bd3bd8eb0a1131d0de
author_id_fullname_str_mv 6734caa6d9a388bd3bd8eb0a1131d0de_***_Feng-yu Wang
author Feng-yu Wang
author2 Xing Huang
Feng-yu Wang
format Journal article
container_title Journal of Mathematical Analysis and Applications
container_volume 514
container_issue 1
container_start_page 126301
publishDate 2022
institution Swansea University
issn 0022-247X
doi_str_mv 10.1016/j.jmaa.2022.126301
publisher Elsevier BV
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
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description 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.
published_date 2022-10-01T12:21:11Z
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score 11.037056

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