On the use of Lyapunov methods in renewal theory
type: Item
instance of: scholarly article
title: On the use of Lyapunov methods in renewal theory
zbMATH Open document ID: 0961.60086
DOI: 10.1016/S0304-4149(98)00068-4
author: T. Konstantopoulos
author: Günter Last
published in: Stochastic Processes and their Applications
publication date: 2001-01-17T00:00:00Z
review text: Let \(N\) denote the random measure with atoms at \(T_n, n\in N\), where \(0<T_1<T_2\dots\) are points of a renewal process. The aim of the paper is the study of the asymptotic behaviour of processes associated with \(N\), in particular, the age process \(\{A_t, t\geq 0 \}\) which is defined as the distance between \(t\) and the first atom of \(N\) before \(t\). Convergence of moments and exponential moments of \(A_t\) to the corresponding stationary moments is proved under suitable conditions, and rates of convergence are studied. Also, rates of convergence for Blackwell's theorem are established.
Mathematics Subject Classification ID: 60K15
Mathematics Subject Classification ID: 60K05
zbMATH DE Number: 1554279
zbMATH Keywords: Markov renewal theory
zbMATH Keywords: rates of convergence
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1554279