An iterative approximation procedure for the distribution of the maximum of a random walk
type: Item
instance of: scholarly article
title: An iterative approximation procedure for the distribution of the maximum of a random walk
zbMATH Open document ID: 0967.60058
DOI: 10.1016/S0167-7152(00)00124-3
published in: Statistics \& Probability Letters
publication date: 2001-09-04T00:00:00Z
review text: Let \(I(F)\) be the distribution function of the maximum of a random walk whose i.i.d. increments have the common d.f. \(F\) and a negative mean. A recursive sequence of embedded random walks is derived whose underlying d.f.'s \(F_k\) converge to the d.f. of the first ladder variable and satisfy \(F\geq F_1\geq F_2\geq \cdots\) on \([0,\infty)\) and \(I(F)= I(F_1)= I(F_2)= \cdots\). By using these random walks, improved upper bounds for the difference of \(I(F)\) and the d.f. of the maximum of the random walk after finitely many steps are obtained.
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60K30
zbMATH DE Number: 1556858
zbMATH Keywords: random walk
zbMATH Keywords: maximum
zbMATH Keywords: approximation
zbMATH Keywords: embedded random walk
author: Wolfgang Stadje
reviewed by: Wolfgang Stadje
MaRDI profile type: Publication
cites work: Q4082108
cites work: Q3841898
cites work: Q5624436
cites work: Bounds for a class of stochastic recursive equations
cites work: A new approach to the Lindley recursion
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description: scientific article; zbMATH DE number 1556858