On local times of self-similar random fields
type: Item
instance of: scholarly article
title: On local times of self-similar random fields
zbMATH Open document ID: 0831.60059
DOI: 10.1007/BF02335392
author: Nijolė Kalinauskaitė
published in: Lithuanian Mathematical Journal
publication date: 1995-09-18T00:00:00Z
review text: The author considers \(\kappa\)-self-similar stochastic fields \(X: \Omega\times \mathbb{R}^N\to \mathbb{R}^d\), i.e. such fields that \(X(c\cdot)\) and \(c^\kappa X(\cdot)\) have the same distribution. In addition, for any \(m\geq 1\) the distribution of the random vector \(\{X(t_1+ s_1)- X(t_1),\dots, X(t_m+ s_m)- X(t_m)\}\), \(t_j,s_j\in \mathbb{R}^N\), does not depend on \(\{t_1,\dots, t_m\}\). Under some restrictions on characteristic functions \(E\exp\{i \sum^k_{j= 1}(z_j, x(s_j))\}\), the author establishes for the field \(X\) the existence of occupation density \(\alpha(x, B)\) that belongs to \(L^2(\mathbb{R}^d, x)\) a.s. Namely, such occupation density, or local time, exists if and only if \(\kappa d< N\). The continuity and Hölder properties of \(\alpha(x, B)\) are also considered.
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 60G18
Mathematics Subject Classification ID: 60J55
zbMATH DE Number: 794513
zbMATH Keywords: self-similar random field
zbMATH Keywords: stationary increments
zbMATH Keywords: local time
zbMATH Keywords: characteristic functions
zbMATH Keywords: occupation density
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
cites work: Q3935962
cites work: Gaussian Processes with Stationary Increments: Local Times and Sample Function Properties
cites work: Harmonic Analysis of Local Times and Sample Functions of Gaussian Processes
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: Hölder conditions for the local times of certain Gaussian processes with stationary increments
cites work: A local time approach to the self-intersections of Brownian paths in space
cites work: Self-intersections of random fields
cites work: Multiple points for the sample paths of the symmetric stable process
full work available at URL: https://doi.org/10.1007/bf02335392
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description: scientific article; zbMATH DE number 794513