Dilated fractional stable motions
type: Item
instance of: scholarly article
title: Dilated fractional stable motions
zbMATH Open document ID: 1055.60041
DOI: 10.1023/B:JOTP.0000020475.95139.37
author: Vladas Pipiras
author: Murad S. Taqqu
published in: Journal of Theoretical Probability
publication date: 2004-08-06T00:00:00Z
review text: The authors present a deep and detailed analysis of dilated fractional stable motions, namely processes which are symmetric \(\alpha\)-stable, self similar, with stationary increments and associated with dissipative flows, assuming the stability exponent \(\alpha\) to be less than 2 so that the variance is infinite and the Gaussian case is excluded. They establish several theorems and give well-chosen illustrating examples. The paper consists of eight sections. After an outline of the general concepts the authors investigate in Section 2 equivalent representations and connections to other processes. Then, in Sections 3 and 4, they describe the space of integrands and lay open the connection to Sobolev spaces. Section 5 is devoted to five examples, the first of these the telecom process. In Sections 6 and 7 questions of uniqueness or non-uniqueness are treated, in a more refined way in Section 7 (with four examples), the proofs being delegated to Section 8.
Mathematics Subject Classification ID: 60G52
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60G18
zbMATH DE Number: 2083460
zbMATH Keywords: self-similar processes with stable increments
zbMATH Keywords: dilated fractional stable motions
zbMATH Keywords: uniqueness
zbMATH Keywords: flows
zbMATH Keywords: the telecom process
zbMATH Keywords: random wavelet expansion
reviewed by: Rudolf Gorenflo
MaRDI profile type: Publication
full work available at URL: b:jotp.0000020475.95139.37
OpenAlex ID: W2043928794
description: scientific article; zbMATH DE number 2083460