On lag increments of a Gaussian process
type: Item
instance of: scholarly article
zbMATH Open document ID: 0972.60019
author: Yong-Kab Choi
author: Jin-Hee Choi
publication date: 2001-03-19T00:00:00Z
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 1579139
zbMATH Keywords: Gaussian process
zbMATH Keywords: stationary increments
zbMATH Keywords: Wiener process
zbMATH Keywords: lag increment
zbMATH Keywords: law of the iterated logarithm
zbMATH Keywords: large deviation probabilities
MaRDI profile type: Publication
title: On lag increments of a Gaussian process
published in: Communications of the Korean Mathematical Society
review text: Let \(X(t)\), \(0\leq t<\infty\), be a centered Gaussian process with stationary increments \(E(X(s)- X(t))^2= C^2_0|s-t|^{2\alpha}\), \(0< \alpha< 1\), and \(X(0)= 0\). It is proved that NEWLINE\[NEWLINE\limsup_{T\to\infty} \sup_{0< t\leq T}|X(T)- X(T- t)|/\sqrt 2 C_0t^\alpha(\log(T/t)+ \log\log t)^{1/2}= 1\quad\text{a.s.}NEWLINE\]NEWLINE Other related a.s. limits are also obtained thus giving a direct extension of \textit{G. Chen}, \textit{F. Kong} and \textit{Z. Lin}'s result [Ann. Probab. 14, 1252-1261 (1986; Zbl 0613.60027)] for lag increments of a Wiener process. The proof is based on upper bounds of large deviation probabilities on suprema of a Gaussian process.
reviewed by: T. Inglot
description: scientific article