Moment generating function of a first hitting place for the integrated Ornstein-Uhlenbeck process
type: Item
instance of: scholarly article
title: Moment generating function of a first hitting place for the integrated Ornstein-Uhlenbeck process
zbMATH Open document ID: 0676.60062
DOI: 10.1016/0304-4149(89)90080-X
author: Mario Lefebvre
published in: Stochastic Processes and their Applications
publication date: 1989-01-01T00:00:00Z
review text: An explicit expression for the moment generating function of x(T) is obtained, when \(y\geq v\geq 0\), where \(T=\min \{t:\) \(y(t)=v\}\), y(t) is an Ornstein-Uhlenbeck process with \(y(0)=y\) and \(x(t)=x+\int^{t}_{0}y(s)ds\), and for the characteristic function of x(T) when y(0)\(\leq v\) \((v>0).\) The expected value of x(T) turns out to be the same in both cases considered.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60E10
zbMATH DE Number: 4107868
zbMATH Keywords: moment generating function
zbMATH Keywords: Ornstein-Uhlenbeck process
zbMATH Keywords: characteristic function
reviewed by: Constantin Vârsan
MaRDI profile type: Publication
cites work: Q3661894
cites work: Q3920398
cites work: Q5528194
cites work: On the First Passage of the Integrated Wiener Process
cites work: Q4087628
cites work: Hitting Lines with Two-Dimensional Brownian Motion
cites work: First-Passage Densities of a Two-Dimensional Process
cites work: A winding problem for a resonator driven by a white noise
cites work: Q5512464
cites work: Hitting spheres with Brownian motion
full work available at URL: 0304-4149(89)90080-x
OpenAlex ID: W2072883368
description: scientific article; zbMATH DE number 4107868