On the time schedule of Brownian Flights

TL;DR

This paper investigates the statistical properties of the duration of Brownian motions initiated near a boundary and stopped upon hitting the boundary again, providing insights into their time schedule.

Contribution

It introduces a detailed analysis of the hitting time distribution for Brownian flights starting close to a boundary, which is a novel focus in stochastic process research.

Findings

Derived explicit formulas for hitting time distributions.

Identified asymptotic behaviors as initial distance approaches zero.

Provided applications to boundary-related stochastic problems.

Abstract

We are interested on the statistics of the duration of Brownian diffusions started at distance \epsilon from a given boundary and stopped when they hit back the interface.