On the sample path behavior of the first passage time process of a Brownian motion with drift
type: Item
instance of: scholarly article
title: On the sample path behavior of the first passage time process of a Brownian motion with drift
zbMATH Open document ID: 0699.60018
author: P. Deheuvels
author: J. G. Steinebach
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1990-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77369
review text: Let \(\{\) W(t), \(t\geq 0\}\) be a Wiener process and consider the Brownian motion \(X(t)=\mu t+\sigma W(t)\) (t\(\geq 0\), \(\mu >0\), \(\sigma\neq 0)\) as well as the first passage time process \(M(t)=\inf \{s\geq 0:\) X(s)\(\geq t\}\) (t\(\geq 0)\). The authors investigate the properties of the increments \[ \Delta (T)=\sup_{0\leq t\leq T-a(T)}(M(t+a(T))-M(T)) \] where \(0<a(T)\leq T\) is a function satisfying some regularity conditions. The main results give a complete enough strong law for the lim sup and lim inf behaviour of \(\Delta\) (T).
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 4147199
zbMATH Keywords: Brownian motion with drift
zbMATH Keywords: strong limit theorems
zbMATH Keywords: first passage time process
reviewed by: Pál Révész
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4147199