Large deviation results for waiting times in repeated experiments
type: Item
instance of: scholarly article
title: Large deviation results for waiting times in repeated experiments
zbMATH Open document ID: 0574.60034
DOI: 10.1007/BF01955038
published in: Acta Mathematica Hungarica
publication date: 1985-01-01T00:00:00Z
review text: Consider an i.i.d. sequence \(Z_ 1,Z_ 2,..\). with a finite set of possible values \(\Sigma\) and let \(A_ i\) \((i=1,...,r)\) be finite sequences of length k over \(\Sigma\). The author presents exact upper and lower exponential bounds for the joint probabilities \(P(\tau_ 1/E\tau_ 1>x_ 1,...,\tau_ r/E\tau_ r>x_ r)\), where \(\tau_ i\) denotes the waiting time until \(A_ i\) occurs as a run in the sequence \(Z_ 1,Z_ 2,...\), and \(x_ 1,...,x_ r\) are arbitrary positive numbers. This is a large deviation type result which, in particular, establishes asymptotic independence and exponentiality of the stopping times \(\tau_ i\).
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60C05
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 3917355
zbMATH Keywords: exact upper and lower exponential bounds
zbMATH Keywords: asymptotic independence and exponentiality
zbMATH Keywords: stopping times
author: Tamás F. Móri
reviewed by: J. G. Steinebach
MaRDI profile type: Publication
cites work: Q5538132
cites work: A martingale approach to the study of occurrence of sequence patterns in repeated experiments
cites work: Asymptotic independence of 'pure head' stopping times
full work available at URL: https://doi.org/10.1007/bf01955038
OpenAlex ID: W2007210410
description: scientific article; zbMATH DE number 3917355