Elements related to the largest complete excursion of a reflected BM stopped at a fixed time. Application to local score

TL;DR

This paper investigates the properties of the largest complete excursion of a reflected Brownian motion stopped at a fixed time, with applications to the analysis of local scores in stochastic processes.

Contribution

It introduces new elements related to the largest complete excursion of reflected Brownian motion and applies these findings to local score analysis.

Findings

Characterization of the largest complete excursion

Application to local score analysis

New theoretical insights into reflected Brownian motion

Abstract

Elements related to the largest complete excursion of a reflected BM stopped at a fixed time. Application to local score.