Rough functions: \(p\)-variation, calculus, and index estimation
type: Item
instance of: scholarly article
title: Rough functions: \(p\)-variation, calculus, and index estimation
zbMATH Open document ID: 1155.26006
published in: Lithuanian Mathematical Journal
publication date: 2008-05-20T00:00:00Z
review text: The author gives an overview of several dissipated results on the \(p\)-variation property of a function. Starting from the fact that a \(p\)-variation gives a convenient way to measure a degree of roughness of a function, the author attempts to show the usefulness of this property in a calculus of rough functions and to review boundedness of \(p\)-variation results for basic classes of stochastic processes. In the last section, two methods of estimating the \(p\)-variation index of a function given by finitely many values are discussed.
reviewed by: Octavian Lipovan
Mathematics Subject Classification ID: 26A42
Mathematics Subject Classification ID: 47H30
Mathematics Subject Classification ID: 60G07
zbMATH DE Number: 5277488
zbMATH Keywords: \(\Phi\)-variation
zbMATH Keywords: interval functions
zbMATH Keywords: refinement Young-Stieltjes integral
zbMATH Keywords: Kolmogorov integral
zbMATH Keywords: product integral
zbMATH Keywords: Nemytskii operator
zbMATH Keywords: integral equations
zbMATH Keywords: sample functions of stochastic processes
zbMATH Keywords: \(p\)-variation index
zbMATH Keywords: Orey index
zbMATH Keywords: oscillation summing index
author: Rimas Norvaiša
MaRDI profile type: Publication
full work available at URL: s10986-006-0015-1
OpenAlex ID: W2091436578
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DOI: 10.1007/S10986-006-0015-1
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