Translator Disclaimer
2015 Probability that the maximum of the reflected Brownian motion over a finite interval $[0,t]$ is achieved by its last zero before $t$.
Sabine Mercier, Agnès Lagnoux, Pierre Vallois
Author Affiliations +
Electron. Commun. Probab. 20: 1-9 (2015). DOI: 10.1214/ECP.v20-4279

Abstract

We calculate the probability $p_c$ that the maximum of a reflected Brownian motion $U$ is achieved on a complete excursion, i.e. $p_c:=P\big(\overline{U}(t)=U^*(t)\big)$ where $\overline{U}(t)$ (respectively $U^*(t)$) is the maximum of the process $U$ over the time interval $[0,t]$ (respectively $\big[0,g(t)\big]$ where $g(t)$ is the last zero of $U$ before $t$).

Citation

Download Citation

Sabine Mercier. Agnès Lagnoux. Pierre Vallois. "Probability that the maximum of the reflected Brownian motion over a finite interval $[0,t]$ is achieved by its last zero before $t$.." Electron. Commun. Probab. 20 1 - 9, 2015. https://doi.org/10.1214/ECP.v20-4279

Information

Accepted: 8 September 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1329.60292
MathSciNet: MR3399813
Digital Object Identifier: 10.1214/ECP.v20-4279

Subjects:
Primary: 60 G 17
Secondary: 60 J 25, 60 J 65

JOURNAL ARTICLE
9 PAGES


SHARE
Back to Top