Komlós-Major-Tusnády approximation under dependence
type: Item
instance of: scholarly article
title: Komlós-Major-Tusnády approximation under dependence
zbMATH Open document ID: 1308.60037
DOI: 10.1214/13-AOP850
author: István Berkes
author: Weidong Liu
author: Wei Biao Wu
published in: The Annals of Probability
publication date: 2014-04-25T00:00:00Z
full work available at URL: https://arxiv.org/abs/1402.6517
full work available at URL: https://projecteuclid.org/euclid.aop/1393251303
review text: The authors of the paper analyze the Komlós-Major-Tusnády (KMT) approximation. They note that the dyadic construction of \textit{J. Komlós} et al. [Z. Wahrscheinlichkeitstheor. Verw. Geb. 32, 111--131 (1975; Zbl 0308.60029); ibid. 34, 33--58 (1976; Zbl 0307.60045)] is highly technical and utilizes conditional large deviation techniques, which makes it very difficult to extend to dependent processes. So, the authors develop a new approximation technique, called triadic decomposition scheme, that enables them to prove the KMT approximation for all \(p >2\) and a large class of dependent sequences under natural moment conditions. Also, the authors give a few examples of applications to ergodic sums, nonlinear time series and Volterra processes.
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 6288294
zbMATH Keywords: KMT approximation
zbMATH Keywords: stationary processes
zbMATH Keywords: strong invariance principle
zbMATH Keywords: dependent sequences
zbMATH Keywords: Wiener process
zbMATH Keywords: nonlinear time series
zbMATH Keywords: ergodic sums
reviewed by: Jurgita Markeviciute
MaRDI profile type: Publication
arXiv ID: 1402.6517
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OpenAlex ID: W3100926372
description: scientific article