Average extrema of a random walk with a negative binomial stopping time
type: Item
instance of: scholarly article
zbMATH Open document ID: 1296.60116
author: David K. Neal
publication date: 2013-12-20T00:00:00Z
full work available at URL: index.html
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 6241506
zbMATH Keywords: simple random walk
zbMATH Keywords: average minimum height
zbMATH Keywords: average maximum height
zbMATH Keywords: negative binomial random variable
zbMATH Keywords: reflection principle
MaRDI profile type: Publication
OpenAlex ID: W2088204410
DOI: 10.12732/IJPAM.V88I3.7
title: Average extrema of a random walk with a negative binomial stopping time
published in: International Journal of Pure and Applied Mathematics
review text: The author considers a simple random walk that moves upward and downward one unit at a time with probability \(p\) and \(1-p\), respectively. Let \(T_{n}\) denote the number of steps taken upon making \(n\) downward movements. Let \(M_{i}\) and \(m_{i}\) be the maximum and minimum heights obtained through \(i\) steps. The paper deals mainly with the expectations \(\operatorname{E}M_{T_{n}}\), \(\operatorname{E}m_{T_{n}-1}\) and \(\operatorname{E}m_{T_{n}}\). A version of a random walk that moves up and down \(j\) units at a time is also considered.
reviewed by: Aurel Spătaru
description: scientific article; zbMATH DE number 6241506