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A Zvonkin's transformation for stochastic differential equations with singular drift and applications

Shao-Qin Zhang, Chenggui Yuan Orcid Logo

Journal of Differential Equations, Volume: 297, Pages: 277 - 319

Swansea University Author: Chenggui Yuan Orcid Logo

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DOI (Published version): 10.1016/j.jde.2021.06.031

Abstract

In this paper, a new Zvonkin-type transformation is given for stochastic differential equations with singular and Lipschitz drifts by establishing the localized $L^p$-$L^q$ estimate and Sobolev estimates for parabolic partial differential equations with a singular first order term and a Lipschitz fi...

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Published in: Journal of Differential Equations
ISSN: 0022-0396
Published: Elsevier BV 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa57821
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first_indexed 2021-09-15T09:01:58Z
last_indexed 2021-12-01T04:17:19Z
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spelling 2021-11-30T16:01:44.8547890 v2 57821 2021-09-09 A Zvonkin's transformation for stochastic differential equations with singular drift and applications 22b571d1cba717a58e526805bd9abea0 0000-0003-0486-5450 Chenggui Yuan Chenggui Yuan true false 2021-09-09 SMA In this paper, a new Zvonkin-type transformation is given for stochastic differential equations with singular and Lipschitz drifts by establishing the localized $L^p$-$L^q$ estimate and Sobolev estimates for parabolic partial differential equations with a singular first order term and a Lipschitz first order term. The associated Krylov's estimate is established. As applications, dimension-free Harnack inequalities are established for stochastic equations with H\"older continuous diffusion coefficient and singular drift term without regularity assumption. Journal Article Journal of Differential Equations 297 277 319 Elsevier BV 0022-0396 Zvonkin&apos;s transformation; singular diffusion processes; Krylov&apos;s estimate; Harnack inequality 5 10 2021 2021-10-05 10.1016/j.jde.2021.06.031 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2021-11-30T16:01:44.8547890 2021-09-09T06:21:36.8768521 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Shao-Qin Zhang 1 Chenggui Yuan 0000-0003-0486-5450 2 57821__20796__984146831f7446c9a5c853d5121c67ca.pdf RIS.pdf 2021-09-09T06:31:56.5064658 Output 408285 application/pdf Accepted Manuscript true 2022-06-29T00:00:00.0000000 ©2021 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 A Zvonkin's transformation for stochastic differential equations with singular drift and applications
spellingShingle A Zvonkin's transformation for stochastic differential equations with singular drift and applications
Chenggui Yuan
title_short A Zvonkin's transformation for stochastic differential equations with singular drift and applications
title_full A Zvonkin's transformation for stochastic differential equations with singular drift and applications
title_fullStr A Zvonkin's transformation for stochastic differential equations with singular drift and applications
title_full_unstemmed A Zvonkin's transformation for stochastic differential equations with singular drift and applications
title_sort A Zvonkin's transformation for stochastic differential equations with singular drift and applications
author_id_str_mv 22b571d1cba717a58e526805bd9abea0
author_id_fullname_str_mv 22b571d1cba717a58e526805bd9abea0_***_Chenggui Yuan
author Chenggui Yuan
author2 Shao-Qin Zhang
Chenggui Yuan
format Journal article
container_title Journal of Differential Equations
container_volume 297
container_start_page 277
publishDate 2021
institution Swansea University
issn 0022-0396
doi_str_mv 10.1016/j.jde.2021.06.031
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
active_str 0
description In this paper, a new Zvonkin-type transformation is given for stochastic differential equations with singular and Lipschitz drifts by establishing the localized $L^p$-$L^q$ estimate and Sobolev estimates for parabolic partial differential equations with a singular first order term and a Lipschitz first order term. The associated Krylov's estimate is established. As applications, dimension-free Harnack inequalities are established for stochastic equations with H\"older continuous diffusion coefficient and singular drift term without regularity assumption.
published_date 2021-10-05T04:13:51Z
_version_ 1763753938180374528
score 11.03559

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