Small time asymptotics for Brownian motion with singular drift

Chen, Zhen-Qing; Fang, Shizan; Zhang, Tusheng

doi:10.1090/proc/14511

Small time asymptotics for Brownian motion with singular drift
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by Zhen-Qing Chen, Shizan Fang and Tusheng Zhang PDF

Proc. Amer. Math. Soc. 147 (2019), 3567-3578 Request permission

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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