Maxima of increments of partial sums for certain subexponential distributions
type: Item
instance of: scholarly article
title: Maxima of increments of partial sums for certain subexponential distributions
zbMATH Open document ID: 1028.60044
DOI: 10.1016/S0304-4149(99)00100-3
published in: Stochastic Processes and their Applications
publication date: 2003-11-03T00:00:00Z
review text: The following result is proved for partial sums \(S_n\) of i.i.d. random variables that exhibit subexponential tails: \[ \lim _{n\to \infty }\left \{ \max _{0\leq j <n} \max _ {1\leq k \leq n - j} \frac {S_{j+k} - S_j}{\varphi (k/ \log n)^{2p - 1} (\log n)^p }\right \} = 1 \text{ a.s.}, \] where \(\varphi \) is a function specified in the paper and \(p > 1.\) Instead of the assumption of existence and finiteness of the moment generating function of the underlying distribution some other moment conditions are considered.
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60G70
zbMATH DE Number: 2000174
zbMATH Keywords: partial sums
zbMATH Keywords: maxima of increments
zbMATH Keywords: subexponential distributions
author: H. Lanzinger
author: Ulrich Stadtmüller
reviewed by: Zuzana Prášková
MaRDI profile type: Publication
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Wikidata QID: Q126819243
full work available at URL: s0304-4149(99)00100-3
OpenAlex ID: W1983318766
description: scientific article; zbMATH DE number 2000174