On the joint distribution of ladder variables of random walk
type: Item
instance of: scholarly article
title: On the joint distribution of ladder variables of random walk
zbMATH Open document ID: 0791.60058
DOI: 10.1007/BF01192558
publication date: 1994-07-14T00:00:00Z
review text: The ladder time \(N\) and ladder height \(H\) of a random walk \(\{S_ n, n \geq 1\}\) as a pair \((N,H)\) lie in the domain of attraction of a bivariate stable law if \(S_ 1\) is in a domain of attraction, as was shown by \textit{P. E. Greenwood}, \textit{E. Omey} and \textit{J. L. Teugels} [Z. Wahrscheinlichkeitstheorie Verw. Geb. 61, 527-539 (1982; Zbl 0493.60072)]. We prove a converse. If \(P(S_ n>0)\) converges and \((N,H)\) lies in a bivariate domain of attraction, then \(S_ 1\) is also in a domain of attraction.
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 569060
zbMATH Keywords: ladder time
zbMATH Keywords: ladder height
zbMATH Keywords: domain of attraction of a bivariate stable law
author: Ronald A. Doney
author: Priscilla Greenwood
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01192558
OpenAlex ID: W2012889700
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 569060