On moduli of continuity for local times of Gaussian processes
type: Item
instance of: scholarly article
title: On moduli of continuity for local times of Gaussian processes
zbMATH Open document ID: 0834.60088
DOI: 10.1016/0304-4149(94)00012-I
published in: Stochastic Processes and their Applications
publication date: 1995-11-14T00:00:00Z
review text: The authors study the sample path properties of increments in \(t\) of the local times \(L(t,x)\) of Gaussian processes with stationary increments and those of stationary Gaussian processes as well. In their study they have in view some well-known fine analytic properties of the moduli in \(t\) of the local time \(l(x,t)\) of a standard Wiener process \(\{W(t), t \geq 0\}\). Also, they present and discuss results which are analogous to some results previously obtained by Hawkes and Perkins. Finally, some results are presented and proved, which are analogous to some results of Perkins, for the local times \(L(x,t)\) of Gaussian processes \(\{X (t), t \geq 0\}\). Some of them do not seem to have been studied much before. In conclusion, upper bounds for moduli of continuity of the local times of Gaussian processes with stationary increments and for those of stationary Gaussian processes are established.
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 803374
zbMATH Keywords: sample path properties
zbMATH Keywords: stationary Gaussian processes
zbMATH Keywords: local times
author: Miklós Csörgo
author: Zhengyan Lin
author: Q. M. Shao
reviewed by: Gabriel V. Orman
MaRDI profile type: Publication
cites work: Q1085881
cites work: Local Times and Sample Function Properties of Stationary Gaussian Processes
cites work: Gaussian Sample Functions: Uniform Dimension and Hölder Conditions Nowhere
cites work: Q5680823
cites work: How big are the increments of the local time of a Wiener process?
cites work: Local Hölder conditions for the local times of certain stationary Gaussian processes
cites work: Sample function properties of multi-parameter stable processes
cites work: Occupation densities
cites work: A lower lipschitz condition for the stable subordinator
cites work: An iterated logarithm law for local time
cites work: Hölder conditions for the local times of certain Gaussian processes with stationary increments
cites work: Some limit theorems for sojourn times of strongly dependent Gaussian processes
cites work: Gaussian processes with stationary increments possessing discontinuous sample paths
cites work: Sample path properties of the local times of strongly symmetric Markov processes via Gaussian processes
cites work: \(p\)-variation of the local times of symmetric stable processes and of Gaussian processes with stationary increments
cites work: Q3948379
cites work: The exact Hausdorff measure of the level sets of Brownian motion
cites work: Bounds for Determinants with Dominant Principal Diagonal
description: scientific article; zbMATH DE number 803374