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Stochastic Differential Equations with Low Regularity Growing Drifts and Applications

Jinlong Wei, Junhao Hu, Chenggui Yuan Orcid Logo

SIAM Journal on Mathematical Analysis, Volume: 57, Issue: 5, Pages: 4867 - 4907

Swansea University Author: Chenggui Yuan Orcid Logo

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DOI (Published version): 10.1137/24m1636939

Abstract

The unique strong solvability as well as the gradient estimates for stochastic differential equations with irregular growing drifts in low regularity Lebesgue--H\"{o}lder spaces $L^q(0,T;{\mathcal C}^\alpha({\mathbb R}^d))$ with $\alpha\in(0,1)$ and $q\in (2/(1+\alpha),2$) is proved, by means o...

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Published in: SIAM Journal on Mathematical Analysis
ISSN: 0036-1410 1095-7154
Published: Society for Industrial & Applied Mathematics (SIAM) 2025
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URI: https://cronfa.swan.ac.uk/Record/cronfa70247
first_indexed 2025-09-02T07:24:26Z
last_indexed 2025-09-02T07:24:26Z
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spelling 2025-09-01T15:15:29.0888055 v2 70247 2025-09-01 Stochastic Differential Equations with Low Regularity Growing Drifts and Applications 22b571d1cba717a58e526805bd9abea0 0000-0003-0486-5450 Chenggui Yuan Chenggui Yuan true false 2025-09-01 MACS The unique strong solvability as well as the gradient estimates for stochastic differential equations with irregular growing drifts in low regularity Lebesgue--H\"{o}lder spaces $L^q(0,T;{\mathcal C}^\alpha({\mathbb R}^d))$ with $\alpha\in(0,1)$ and $q\in (2/(1+\alpha),2$) is proved, by means of the It\^{o}--Tanaka trick. As applications, we establish an $L^2$-transportation cost inequality for these stochastic differential equations first, and then establish the unique strong solvability for a class of stochastic transport equations. Journal Article SIAM Journal on Mathematical Analysis 57 5 4867 4907 Society for Industrial & Applied Mathematics (SIAM) 0036-1410 1095-7154 Low regularity growing drift, Unique strong solvability, Itˆo–Tanaka trick, Kolmogorov equation, L2-transportation cost inequality 31 10 2025 2025-10-31 10.1137/24m1636939 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2025-09-01T15:15:29.0888055 2025-09-01T10:36:19.2132569 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Jinlong Wei 1 Junhao Hu 2 Chenggui Yuan 0000-0003-0486-5450 3 70247__35005__8ed3e480ee0c4ed6ab0dc52b203b35d8.pdf Web-1.pdf 2025-09-01T10:44:44.1978138 Output 456992 application/pdf Accepted Manuscript true Author accepted manuscript document released under the terms of a Creative Commons CC-BY licence using the Swansea University Research Publications Policy (rights retention). true eng https://creativecommons.org/licenses/by/4.0/deed.en
title Stochastic Differential Equations with Low Regularity Growing Drifts and Applications
spellingShingle Stochastic Differential Equations with Low Regularity Growing Drifts and Applications
Chenggui Yuan
title_short Stochastic Differential Equations with Low Regularity Growing Drifts and Applications
title_full Stochastic Differential Equations with Low Regularity Growing Drifts and Applications
title_fullStr Stochastic Differential Equations with Low Regularity Growing Drifts and Applications
title_full_unstemmed Stochastic Differential Equations with Low Regularity Growing Drifts and Applications
title_sort Stochastic Differential Equations with Low Regularity Growing Drifts and Applications
author_id_str_mv 22b571d1cba717a58e526805bd9abea0
author_id_fullname_str_mv 22b571d1cba717a58e526805bd9abea0_***_Chenggui Yuan
author Chenggui Yuan
author2 Jinlong Wei
Junhao Hu
Chenggui Yuan
format Journal article
container_title SIAM Journal on Mathematical Analysis
container_volume 57
container_issue 5
container_start_page 4867
publishDate 2025
institution Swansea University
issn 0036-1410
1095-7154
doi_str_mv 10.1137/24m1636939
publisher Society for Industrial & Applied Mathematics (SIAM)
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 0
active_str 0
description The unique strong solvability as well as the gradient estimates for stochastic differential equations with irregular growing drifts in low regularity Lebesgue--H\"{o}lder spaces $L^q(0,T;{\mathcal C}^\alpha({\mathbb R}^d))$ with $\alpha\in(0,1)$ and $q\in (2/(1+\alpha),2$) is proved, by means of the It\^{o}--Tanaka trick. As applications, we establish an $L^2$-transportation cost inequality for these stochastic differential equations first, and then establish the unique strong solvability for a class of stochastic transport equations.
published_date 2025-10-31T08:24:40Z
_version_ 1863154590820597760
score 11.105427

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