A tightness criterion in Besov-Orlicz spaces and applications to the problem of occupation times
type: Item
instance of: scholarly article
title: A tightness criterion in Besov-Orlicz spaces and applications to the problem of occupation times
zbMATH Open document ID: 1252.60032
author: Mohamed Ait Ouahra
author: Abdelghani Kissami
author: Aissa Sghir
published in: Annales Mathématiques Blaise Pascal
publication date: 2011-12-19T00:00:00Z
full work available at URL: https://eudml.org/doc/219844
review text: The authors give a brief review of fractional derivatives (in one dimension) and Besov-Orlicz spaces, in particular the Haar-Schauder wavelet representation due to \textit{Z. Ciesielski, G. Kerkyacharian} and \textit{B. Roynette} [Stud. Math. 107, No. 2, 171--204 (1993; Zbl 0809.60004)]. Then they derive a tightness result for(sequences of) processes in Besov-Orlicz spaces. This leads to a further proof of Kolmogorov-Chentsov-type path regularity theorems. This result is subsequently applied to Besov-Orlicz regularity of Gaussian processes, of local times of rotationally symmetric \(\alpha\)-stable Lévy processes and their fractional (in time) derivatives. Finally, limit theorems for expressions of the form \(\lambda^{(\alpha-1-\gamma)/\alpha}\int_0^{\lambda t} f(X_s)\,ds\), \((\lambda\to\infty)\) where \(f\) is a fractional derivative of some Hölder function, in Besov norm are established.
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60J55
zbMATH DE Number: 5989456
zbMATH Keywords: Besov space
zbMATH Keywords: Orlicz space
zbMATH Keywords: stable processes
zbMATH Keywords: local time
zbMATH Keywords: fractional derivative
reviewed by: R. L. Schilling
MaRDI profile type: Publication
OpenAlex ID: W2028736617
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DOI: 10.5802/AMBP.301
description: scientific article; zbMATH DE number 5989456