Large and moderate deviations for moving average processes
type: Item
instance of: scholarly article
title: Large and moderate deviations for moving average processes
zbMATH Open document ID: 1002.60028
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 2003-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/73539
review text: Let \(\{\omega_i\}\) be iid random variables. Define \(X_k = \sum_{i=-\infty}^{\infty} a_{i+k}\omega_i\), \(S_n=\sum_{k=1}^n X_k\). Assume that the following conditions are satisfied: (H1) \(\sum a_i^2<\infty\), \(E\omega_i=0\), \(E\omega_i^2=1\), \(|\omega_i|\leq C\) where \(C\) is a constant; (H2) the spectral density of \(\{X_t\}\) is continuous at 0 and square integrable. The authors prove that then \(S_n/n\) satisfies a large deviation principle with speed \(n\). If \(\{b_n\}\) is a sequence such that \(b_n\to \infty\), \(b_n/\sqrt n\to 0\), then \(S_n/(b_n\sqrt n)\) also satisfies a large deviation principle, this time with the speed \(b_n^2\). In the both cases the good rate functions are given.
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 1796102
zbMATH Keywords: moving average process
zbMATH Keywords: large deviations
zbMATH Keywords: moderate deviations
zbMATH Keywords: good rate function
zbMATH Keywords: Hoeffding inequality
author: Hacène Djellout
author: Arnaud Guillin
reviewed by: Jiří Anděl
MaRDI profile type: Publication
OpenAlex ID: W2322091505
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DOI: 10.5802/AFST.982
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description: scientific article; zbMATH DE number 1796102