On large increments of \(l^ p\)-valued Gaussian processes
type: Item
instance of: scholarly article
title: On large increments of \(l^ p\)-valued Gaussian processes
zbMATH Open document ID: 0880.60038
published in: Chinese Annals of Mathematics. Series B
publication date: 1997-08-07T00:00:00Z
review text: Let \((Y(t), t\geq 0)= (X_k(t), t\geq 0)^\infty_{k=1}\) be a sequence of independent Gaussian processes with \(EX_k(t)= 0\) and stationary increments \(\sigma^2_k(h)= E(X_k(t+h)- X_k(t))^2\), where \(\sigma_k(h)\) is assumed to be a nondecreasing continuous function for each \(k\geq 1\). Put \(\sigma(p,h)= \left(\sum^\infty_{k=1}\sigma^p_k(h)\right)^{1/p}\), \(p\geq 1\). If \(\sigma(p,h)<\infty\), then \(Y(t+h)- Y(t)\in\ell^p\), \(1\leq p<\infty\), almost surely for fixed \(t\) and \(h\). The author establishes the large increment results for \((Y(t), t\geq 0)\) with bounded \(\sigma(p,h)\). For example, \(\sigma(p,h)\) is bounded for the Ornstein-Uhlenbeck processes.
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 1045556
zbMATH Keywords: infinite-dimensional Gaussian process
zbMATH Keywords: large increment
zbMATH Keywords: Ornstein-Uhlenbeck processes
author: Zhengyan Lin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1045556