The successive hitting times for the integrated Brownian motion
type: Item
instance of: scholarly article
title: The successive hitting times for the integrated Brownian motion
zbMATH Open document ID: 0877.60054
DOI: 10.1016/S0246-0203(97)80114-8
author: A. Lachal
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1997-11-26T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77559
review text: Let \(B_t\) be the real Brownian motion, and \(X_t: =x+\int^t_0 (y+B_s)ds\). Set \(\tau_{n+1}: =\min \{t> \tau_n\mid X_t=0\}\) and \(\beta_n: =|B_{\tau_n} |\). The author computes the Kontorovich-Lebedev transform of \((\tau_n,\beta_n)\) in the two cases: \(\tau_0 =0\) or 1, and then deduces rather complicated formulas for the density of \((\tau_n, \beta_n)\), thereby completing an ancient article by H. P. McKean.
reviewed by: Jacques Franchi
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 999601
zbMATH Keywords: hitting times
zbMATH Keywords: Mellin transform
zbMATH Keywords: Brownian motion
zbMATH Keywords: Kontorovich-Lebedev transform
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 999601