Time of exit of a semicontinuous process with boundary
type: Item
instance of: scholarly article
title: Time of exit of a semicontinuous process with boundary
zbMATH Open document ID: 0635.60099
DOI: 10.1007/BF01060946
author: V. N. Suprun
author: V. M. Shurenkov
published in: Ukrainian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: Let \((\xi (t))_{t\geq 0}\) be a homogeneous process with independent increments and positive jumps, the paths of which are right continuous. Loosely speaking, it is possible to define on the phase space [0,\(\infty)\) a homogeneous Markov process \((x(t))_{t\geq 0}\) as follows: Up to the moment the \(\xi\)-process reaches the null level, the increments of both processes coincide. Then the x-process remains in this state a positive time \(\tau_{0+}\) with a parameter 1/\(\mu\), and at a (random) moment \(\tau_{0+}\) leaves it, having a positive increment \(\xi\) (distributed according to a given function F) which does not depend on the previous history of the process. The aim of the paper is to study the limit of the repartition of the random variable \(\tau_ T=\inf \{t:x(t)\geq T\}\) as \(t\to \infty\).
reviewed by: S.Grigorescu
Mathematics Subject Classification ID: 60K15
Mathematics Subject Classification ID: 60K10
Mathematics Subject Classification ID: 60J99
zbMATH DE Number: 4034827
zbMATH Keywords: homogeneous process with independent increments
zbMATH Keywords: positive jumps
zbMATH Keywords: limit of the repartition
MaRDI profile type: Publication
cites work: Q3658854
cites work: Q3321197
cites work: Strong Renewal Theorems with Infinite Mean
full work available at URL: https://doi.org/10.1007/bf01060946
OpenAlex ID: W2062296815
description: scientific article; zbMATH DE number 4034827