On one-sided strong laws for large increments of sums
type: Item
instance of: scholarly article
title: On one-sided strong laws for large increments of sums
zbMATH Open document ID: 0893.60016
DOI: 10.1016/S0167-7152(97)00113-2
author: Andrey Frolov
published in: Statistics \& Probability Letters
publication date: 1998-07-22T00:00:00Z
review text: Results for increments of sums of random variables can be applied to study asymptotic behavior of increments of renewal processes, compound sum processes and several statistics. Let \(\{X_i, i\geq 1\}\) be a sequence of i.i.d. random variables with partial sums \(S_n\). The asymptotic behavior of maximal increments of partial sums over time subintervals \(a_n, a_n\leq n\), namely \(U_n= \max_{1\leq k\leq n-a_n} (S_{k+a_n} - S_k)\) is studied. Necessary and sufficient conditions for one-sided strong law of large numbers and the law of iterated logarithm for \(U_n\) are obtained. The aim of the paper is to investigate asymptotics of large increments when trajectories of \(S_n\) have large jumps only in one direction. Then the sums cannot be well approximated by a Wiener process, so strong invariance principles do not work. Large deviation techniques are used.
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 1124491
zbMATH Keywords: law of iterated logarithm
zbMATH Keywords: one-sided strong law of large numbers
zbMATH Keywords: large deviations
zbMATH Keywords: moderate deviations
reviewed by: Andrei Volodin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1124491