Stochastic equations with low regularity drifts Article Swipe

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Jinlong Wei , Junhao Hu , Chenggui Yuan ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2310.00421

By using the Itô-Tanaka trick, we prove the unique strong solvability as well as the gradient estimates for stochastic differential equations with irregular drifts in low regularity Lebesgue-Hölder space $L^q(0,T;{\mathcal C}_b^α({\mathbb R}^d))$ with $α\in(0,1)$ and $q\in (2/(1+α),2$). As applications, we show the unique weak and strong solvability for stochastic transport equations driven by the low regularity drift with $q\in (4/(2+α),2$) as well as the local Lipschitz estimate for stochastic strong solutions.

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Lipschitz Continuity

Mathematics

Mathematical Analysis

Computer Science

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Lipschitz continuity Stochastic differential equation Mathematics Space (punctuation) Standard probability space Mathematical analysis Lebesgue integration Pure mathematics Applied mathematics Computer science Operating system

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2310.00421
PDF: https://arxiv.org/pdf/2310.00421
OA Status: green
Cited By: 1
Related Works: 10
OpenAlex ID: https://openalex.org/W4387323485

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DOI: https://doi.org/10.48550/arxiv.2310.00421

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Title: Stochastic equations with low regularity drifts

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Type: preprint

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Language: en

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Publication year: 2023

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Publication date: 2023-09-30

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Authors: Jinlong Wei, Junhao Hu, Chenggui Yuan

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Landing page: https://arxiv.org/abs/2310.00421

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PDF URL: https://arxiv.org/pdf/2310.00421

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Concepts: Lipschitz continuity, Stochastic differential equation, Mathematics, Space (punctuation), Standard probability space, Mathematical analysis, Lebesgue integration, Pure mathematics, Applied mathematics, Computer science, Operating system

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Cited by: 1

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