Extremes of Markov sequences
type: Item
instance of: scholarly article
title: Extremes of Markov sequences
zbMATH Open document ID: 0826.60040
DOI: 10.1016/0378-3758(94)00070-0
author: George Haiman
author: Maxime Kiki
author: Madan L. Puri
published in: Journal of Statistical Planning and Inference
publication date: 1995-11-14T00:00:00Z
review text: For a stationary Markov sequence \(X_j\), \(j \geq 0\), with transition density \(f(x,y)\), the authors estimate the maximum over \(u_n \leq z \leq \omega\) of \(|P (\max (X_0, X_1, \ldots, X_n) < z) - P^{n + 1} (X_0 < z) |\), where \(\omega = \sup \{u : P(X_0 < u) < 1\}\) and \(u_n\) is defined by \(P(X_0 > u_n) = 1/n\), and \(f(x,y)\) is assumed to satisfy a uniform boundedness property in \(x\). In some particular cases, the estimate is shown to be of the magnitude \((\log n)^{3/2}/n^{1/2}\).
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 60J10
zbMATH DE Number: 758079
zbMATH Keywords: asymptotic independence
zbMATH Keywords: uniformly bounded transition
zbMATH Keywords: stationary Markov sequence
reviewed by: Janos Galambos
MaRDI profile type: Publication
full work available at URL: 0378-3758(94)00070-0
OpenAlex ID: W2003751184
cites work: Q3026011
cites work: Q4040329
cites work: Q3938285
cites work: An asymptotic independent representation in limit theorems for maxima of nonstationary random sequences
cites work: Extreme values for stationary and Markov sequences
cites work: Maxima and exceedances of stationary Markov chains
cites work: High-Level exceedances of regenerative and semi-stationary processes
cites work: The extremal index for a Markov chain
description: scientific article; zbMATH DE number 758079