Asymptotic estimates of the distribution of Brownian hitting time of a disc

TL;DR

This paper derives detailed asymptotic estimates for the distribution of the first hitting time of a disc by two-dimensional Brownian motion, providing uniform results across different starting points.

Contribution

It presents new asymptotic estimates for the hitting time distribution of a disc by Brownian motion, based on Laplace transform inversion techniques.

Findings

Asymptotic formulas for the hitting time density

Uniform estimates valid for various starting points

Enhanced understanding of Brownian motion hitting times

Abstract

The distribution of the first hitting time of a disc for the standard two dimensional Brownian motion is computed. By investigating the inversion integral of its Laplace transform we give fairy detailed asymptotic estimates of its density valid uniformly with respect to the point where the Brownian motion starts from.