Exact expressions for moments of ladder heights
type: Item
instance of: scholarly article
title: Exact expressions for moments of ladder heights
zbMATH Open document ID: 1232.60034
DOI: 10.1134/S106456240806029X
published in: Doklady Mathematics
publication date: 2011-06-08T00:00:00Z
review text: Let \((S_n)_{n\geq 0}\) be a zero-delayed random walk with i.i.d. increments. The paper provides explicit expressions for \(\operatorname{E}Z^m\), \(m\in\mathbb{N}\), where \(Z\) is the first ladder height. These expressions take different forms depending on whether \(\operatorname{E}S_1<0\), \(=0\), or \(>0\). Although the resulting formulae are complicated, they represent the moments of the ladder height in terms of the distribution of \(S_1\) which form the main achievement of the paper. Remark. The paper only announces results. No proofs are given.
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60E10
zbMATH DE Number: 5905472
zbMATH Keywords: characteristic function
zbMATH Keywords: ladder height
zbMATH Keywords: random walk
author: Sergei Nagaev
reviewed by: Alexander Iksanov
MaRDI profile type: Publication
cites work: Q5538132
cites work: Moments of ladder variables for driftless random walks
cites work: Asymptotic moments of random walks with applications to ladder variables and renewal theory
cites work: Q3243274
full work available at URL: s106456240806029x
OpenAlex ID: W2755873541
description: scientific article; zbMATH DE number 5905472