Asymptotics of exponential moments of a weighted local time of a Brownian motion with small variance

TL;DR

This paper investigates the asymptotic behavior of weighted local times of scaled Brownian motion as the scaling parameter approaches zero, providing large deviation estimates.

Contribution

It introduces a large deviation estimate for the weighted local time of a small-variance Brownian motion, advancing understanding of its asymptotic properties.

Findings

Established large deviation estimates for weighted local times

Characterized asymptotic behavior as variance tends to zero

Provided mathematical framework for small-variance Brownian analysis

Abstract

We prove a large deviation type estimate for the asymptotic behavior of a weighted local time of $\varepsilon W$ as $\varepsilon\to0$.