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Stochastic differential equations with critically low regularity growing drift

Jinlong Wei, Junhao Hu, Chenggui Yuan Orcid Logo

Journal of Differential Equations, Volume: 440, Issue: 2, Start page: 113453

Swansea University Author: Chenggui Yuan Orcid Logo

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DOI (Published version): 10.1016/j.jde.2025.113453

Abstract

We obtain the existence and uniqueness of stochastic flows of homeomorphisms for a class of stochastic differential equations driven by the low regularity growing drift in critical Lorentz-Hölder space Lq,1([0,T]; Cl 2/q −1 (Rd)) (q ∈ (1, 2)). Moreover, we prove that the unique stochastic flow of ho...

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Published in: Journal of Differential Equations
ISSN: 0022-0396 1090-2732
Published: Elsevier Inc 2025
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URI: https://cronfa.swan.ac.uk/Record/cronfa69562
Abstract: We obtain the existence and uniqueness of stochastic flows of homeomorphisms for a class of stochastic differential equations driven by the low regularity growing drift in critical Lorentz-Hölder space Lq,1([0,T]; Cl 2/q −1 (Rd)) (q ∈ (1, 2)). Moreover, we prove that the unique stochastic flow of homeomorphisms is weakly differentiable with respect to the spatial variables.
Keywords: Low regularity growing drift; Stochastic flow; Lorentz-Hölder space
College: Faculty of Science and Engineering
Funders: Jinlong Wei was partly supported by the National Natural Science Foundation of China grant 12171247. Junhao Hu was partially supported by the National Natural Science Foundation of China grant 62373383 and the Fundamental Research Funds for the Central Universities of South-Central Minzu University grants KTZ20051 and CZT20020.
Issue: 2
Start Page: 113453

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