Block records and maxima of the increments of the Wiener process
type: Item
instance of: scholarly article
title: Block records and maxima of the increments of the Wiener process
zbMATH Open document ID: 0986.60032
DOI: 10.1016/S0378-3758(99)00076-2
author: George Haiman
published in: Journal of Statistical Planning and Inference
publication date: 2002-05-23T00:00:00Z
review text: Let \(\{W(t), t\geq 0\}\), \(W(0)=0,\) be the Wiener process. The basic result of this paper consists in proving that there exists a r.v. \(N\) and a sequence \(\{Z_n \}\) of i.i.d. random variables such that a.s. for \(N\geq n\) the following equality is true \[ \max_{0\leq t\leq n}(W(t)-W(t+1))=\max(Z_1,\ldots ,Z_n). \]
Mathematics Subject Classification ID: 60G10
zbMATH DE Number: 1436935
zbMATH Keywords: increments of Wiener process
zbMATH Keywords: block record
zbMATH Keywords: l-dependent sequences
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1436935