First exit time from a bounded interval for a certain class of additive functionals of Brownian motion
type: Item
instance of: scholarly article
title: First exit time from a bounded interval for a certain class of additive functionals of Brownian motion
zbMATH Open document ID: 0978.60093
DOI: 10.1023/A:1007810528683
author: A. Lachal
published in: Journal of Theoretical Probability
publication date: 2002-01-15T00:00:00Z
review text: Let \((B_t)_{t\geq 0}\) be a standard Brownian motion starting from \(y\) and \(X_t\) be the process defined by \(X_t=x+\int^t_0V(B_s)ds\) for \(x\in (a, b)\), with \(V(z)=z^{\gamma}\) if \(z\geq 0\), \(V(z)=-K(-z)^{\gamma}\) if \(z<0\), where \(\gamma\) and \(K\) are given positive constants. Set \(\tau_{ab}=\inf\{t>0: X_t\notin(a, b)\}\), and \(\sigma_0= \inf\{t>0: B_t=0\}\). The author studies (1) the moments of the random variables \(B_{\tau_{ab}}\) and \(B_{\tau_{ab}\wedge\sigma_0}\); (2) the joint moments of \(\tau_{ab}\) and \(B_{\tau_{ab}}\), and those of \(\tau_{ab}\wedge\sigma_0\) and \(B_{\tau_{ab}\wedge\sigma_0}\); (3) the laws of the random variables \(B_{\tau_{ab}}\) and \(B_{\tau_{ab}\wedge\sigma_0}\).
reviewed by: Renming Song
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 1552708
zbMATH Keywords: first exit time
zbMATH Keywords: excursion process
zbMATH Keywords: Abel's integral equation
zbMATH Keywords: hypergeometric functions
MaRDI profile type: Publication
Recommended article: Some explicit distributions related to the first exit time from a bounded interval for certain functionals of Brownian motion
Recommended article: The first exit time of a Brownian motion from an unbounded convex domain
Recommended article: Q4900627
Recommended article: Temps de sortie d’un intervalle borné pour l’intégrale du mouvement brownien
Recommended article: The first exit time of a Brownian motion from the Minimum and maximum parabolic domains
Recommended article: On the first hitting time and the last exit time for a Brownian motion to/from a moving boundary
Recommended article: Domain functionals and exit times for Brownian motion
Recommended article: The First Exit Time of Fractional Brownian Motion from a Parabolic Domain
description: scientific article; zbMATH DE number 1552708