A limit theorem for sums of random number of i.i.d. random variables and its application to occupation times of Markov chains
type: Item
instance of: scholarly article
title: A limit theorem for sums of random number of i.i.d. random variables and its application to occupation times of Markov chains
zbMATH Open document ID: 0568.60039
author: Yuji Kasahara
published in: Journal of the Mathematical Society of Japan
publication date: 1985-01-01T00:00:00Z
review text: Let \(\{(\xi_ i,\tau_ i)\}^{\infty}_{i=1}\) be a sequence of independent, identically distributed random variables with values in \({\mathbb{R}}\times [0,\infty)\). (We do not assume that \(\{\tau_ i\}_ i\) is independent of \(\{\xi_ i\}_ i.)\) A functional limit theorem for the following process is proved. \(S(t)=\xi_ 1+\xi_ 2+...+\xi_{T(t)},\) \(t\geq 0\), where T(t) is the right-continuous inverse of \(U(t)=\tau_ 1+\tau_ 2+...\tau_{[t]},\) \(t\geq 0\). As an application the occupation-time problem for Markov chains is considered.
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60J10
zbMATH DE Number: 3907476
zbMATH Keywords: functional limit theorem
zbMATH Keywords: occupation-time problem
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/03720197
OpenAlex ID: W2100659943
DOI: 10.2969/JMSJ/03720197
description: scientific article; zbMATH DE number 3907476