Small time asymptotics for Brownian motion with singular drift

Abstract

We establish a small time large deviation principle and a Varadhan type asymptotics for Brownian motion with singular drift on $\bR^d$ with $d\ge 3$ whose infinitesimal generator is $\frac{1}{2}\Delta +\mu \cdot \nabla$, where each ${\mu }_i$ of $\mu =({\mu }_1,\cdots ,{\mu }_d)$ is a measure in some suitable Kato class.

References in corpus (1)

• An integrated version of Varadhan's asymptotics for lower-order perturbations of strong local Dirichlet forms