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Stochastic Differential Equations with Low Regularity Growing Drifts and Applications
SIAM Journal on Mathematical Analysis, Volume: 57, Issue: 5, Pages: 4867 - 4907
Swansea University Author:
Chenggui Yuan
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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...
| Published in: | SIAM Journal on Mathematical Analysis |
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| ISSN: | 0036-1410 1095-7154 |
| Published: |
Society for Industrial & Applied Mathematics (SIAM)
2025
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa70247 |
| 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 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. |
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| Keywords: |
Low regularity growing drift, Unique strong solvability, Itˆo–Tanaka trick, Kolmogorov equation, L2-transportation cost inequality |
| College: |
Faculty of Science and Engineering |
| Issue: |
5 |
| Start Page: |
4867 |
| End Page: |
4907 |