Small time asymptotics for Brownian motion with singular drift
Résumé
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.