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Small time asymptotics for Brownian motion with singular drift


Authors: Zhen-Qing Chen, Shizan Fang and Tusheng Zhang
Journal: Proc. Amer. Math. Soc. 147 (2019), 3567-3578
MSC (2010): Primary 60H15; Secondary 93E20, 35R60
DOI: https://doi.org/10.1090/proc/14511
Published electronically: March 21, 2019
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Abstract | References | Similar Articles | Additional Information

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.


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Additional Information

Zhen-Qing Chen
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195; School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, People’s Republic of China
Email: zqchen@uw.edu

Shizan Fang
Affiliation: Department of Mathematics, University of Bourgogne, 21078 Dijon, France
Email: shizan.fang@u-bourgogne.fr

Tusheng Zhang
Affiliation: School of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, England; School of Mathematics, University of Science and Technology of China, Hefei, People’s Republic of China
Email: tusheng.zhang@manchester.ac.uk

DOI: https://doi.org/10.1090/proc/14511
Keywords: Kato class measure, heat kernel, small time large deviation, small time asymptotics
Received by editor(s): June 25, 2018
Received by editor(s) in revised form: December 7, 2018
Published electronically: March 21, 2019
Additional Notes: This work was partially supported by Simons Foundation Grant 520542 and NNSF of China (11671372, 11431014, 11401557, 11731009, 11721101).
Communicated by: David Levin
Article copyright: © Copyright 2019 American Mathematical Society