On the expected time of the first occurrence of every k bit long patterns in the symmetric Bernoulli process
type: Item
instance of: scholarly article
title: On the expected time of the first occurrence of every k bit long patterns in the symmetric Bernoulli process
zbMATH Open document ID: 0609.60015
DOI: 10.1007/BF01949147
published in: Acta Mathematica Hungarica
publication date: 1986-01-01T00:00:00Z
review text: In a symmetric Bernoulli process (i.e. an infinite sequence of independent coin tossings) let \(T_ k\) denote the first time when every k bit long pattern has already appeared. As the main result of the paper, an elementary proof is given to the following inequality: \[ 2^ k(\ln 2^ k-\ln k+O(k^{-1}))\leq E(T_ k)\leq 2^{k+2}(\ln 2^ k+C+O(2^{- k})), \] where C stands for the Euler constant.
Mathematics Subject Classification ID: 60C05
zbMATH DE Number: 3986268
zbMATH Keywords: stopping time
zbMATH Keywords: symmetric Bernoulli process
zbMATH Keywords: Euler constant
author: András A. Benczúr
reviewed by: Tamás F. Móri
MaRDI profile type: Publication
cites work: A martingale approach to the study of occurrence of sequence patterns in repeated experiments
description: scientific article; zbMATH DE number 3986268