Some results on fractional Brownian sheets and their local times
type: Item
instance of: scholarly article
title: Some results on fractional Brownian sheets and their local times
zbMATH Open document ID: 1158.60010
author: Zong-Mao Cheng
author: Zhengyan Lin
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2008-10-27T00:00:00Z
review text: Let \(B^H_0=\{ B^H_0(t), t\in\mathbb R_+^N\}\) be a real-valued fractional Brownian sheet. Define the \((N, d)\)-Gaussian random field \(B^H\) by \[ B^H(t)= (B^H_1(t),\dots, B^H_d(t)), \quad t \in\mathbb R^N_+, \] where \(B^H_1,\dots,B^H_d\) are independent copies of \(B_0^H\). The existence and joint continuity of local times of \(B^H\) is proven in some given conditions in [\textit{Y. Xiao} and \textit{T. Zhang}, Probab. Theory Relat. Fields 124, No.~2, 204--226 (2002; Zbl 1009.60024)]. The authors study further properties of the local times of \(B^H\), such as the moments of increments of local times, the large increments and the maximum moduli of continuity of local times and as a result, we answer the questions posed in [loc. cit.].
reviewed by: Tae Il Jeon
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 5357873
zbMATH Keywords: Fractional Brownian sheet
zbMATH Keywords: local time
zbMATH Keywords: Hausdorff measure
MaRDI profile type: Publication
full work available at URL: s10255-007-7009-6
OpenAlex ID: W2022991606
cites work: The uniform dimension of the level sets of a Brownian sheet
cites work: Q3935962
cites work: Continuity of Gaussian local times
cites work: Joint continuity of Gaussian local times
cites work: On moduli of continuity for local times of Gaussian processes
cites work: Q4231627
cites work: Sample function properties of multi-parameter stable processes
cites work: Occupation densities
cites work: A local time analysis of intersections of Brownian paths in the plane
cites work: Limsup random fractals
cites work: Q4266067
cites work: Small deviations for some multi-parameter Gaussian processes
cites work: Multiparameter Fractional Brownian Motion And Quasi-Linear Stochastic Partial Differential Equations
cites work: Sample functions of the \(N\)-parameter Wiener process
cites work: Q4160169
cites work: Self-intersections of random fields
cites work: Q3997782
cites work: Hausdorff measure of trajectories of multiparameter fractional Brownian motion
cites work: Hölder conditions for the local times and the Hausdorff measure of the level sets of Gaussian random fields
cites work: Local times of fractional Brownian sheets
DOI: 10.1007/S10255-007-7009-6
description: scientific article; zbMATH DE number 5357873