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Small time asymptotics for Brownian motion with singular drift

Zhen-Qing Chen 1, 2 Shizan Fang 3 Tusheng Zhang 4, 5
1 Department of Mathematics [Seattle]
2 School of Mathematics and Statistics [Beijing]
3 IMB - Institut de Mathématiques de Bourgogne [Dijon]
4 School of Mathematics - Department of Mathematics [Manchester]
5 School of Mathematical Science, University of Science and Technology of China, Hefei, 230026, China
Abstract : We establish a small time large deviation principle and a Varadhan type asymptotics for Brownian motion with singular drift on $ \mathbb{R}^d$ with $ d\geq 3$ whose infinitesimal generator is $ \frac 12 \Delta + \mu \cdot \nabla $, where each $ \mu _i$ of $ \mu = (\mu _1, \ldots , \mu _d)$ is a measure in some suitable Kato class.
Keywords : Kato class measure heat kernel small time large deviation small time asymptotics diffusion-processes behavior
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Article dans une revue
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-02316412
Contributeur : Imb - Université de Bourgogne <>
Soumis le : mardi 15 octobre 2019 - 11:52:30
Dernière modification le : lundi 27 janvier 2020 - 09:54:04

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UNIV-BOURGOGNE | INSMI | CNRS | IMB_UMR5584

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Zhen-Qing Chen, Shizan Fang, Tusheng Zhang. Small time asymptotics for Brownian motion with singular drift. Proceedings of the American Mathematical Society, American Mathematical Society, 2019, 147 (8), pp.3567-3578. ⟨10.1090/proc/14511⟩. ⟨hal-02316412⟩

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