The structure of self-similar stable mixed moving averages
type: Item
instance of: scholarly article
title: The structure of self-similar stable mixed moving averages
zbMATH Open document ID: 1016.60057
author: Vladas Pipiras
author: Murad S. Taqqu
published in: The Annals of Probability
publication date: 2003-05-06T00:00:00Z
review text: A symmetric \(\alpha\)-stable self-similar process with stationary increments \(X_\alpha\) is considered given by the mixed moving average \[ X_{\alpha(t)}=\int_X\int_R(G(x,t+u)-G(x,u))M_{\alpha}(dx,du), \] where \(M_{\alpha}\) is a random measure with the Lebesgue control measure. It is shown that \(X_{\alpha}\) can be decomposed into a sum of three independent processes \(X^{(1)}\), \(X^{(2)}\), \(X^{(3)}\), where \(X^{(1)}\) is generated by a nonsingular dissipative flow, \(X^{(2)}\) and \(X^{(3)}\) are generated by a conservative nonsingular flow. Processes \(X^{(1)}\) and \(X^{(2)}\) are described in terms of integrals by stochastic measures. Some examples of \(X^{(3)}\) are given.
Mathematics Subject Classification ID: 60G52
Mathematics Subject Classification ID: 60G18
Mathematics Subject Classification ID: 60G10
zbMATH DE Number: 1906072
zbMATH Keywords: stable self-similar processes with stationary increments
zbMATH Keywords: dissipative and conservative flows
zbMATH Keywords: cocycles
zbMATH Keywords: semi-additive functions
reviewed by: R. E. Maiboroda
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1023481011
OpenAlex ID: W2108545098
cites work: Q4726487
cites work: Q4218898
cites work: Characterization of linear and harmonizable fractional stable motions
cites work: Construction of stationary self-similar generalized fields by random wavelet expansion
cites work: Log-fractional stable processes
cites work: Ergodic theorems. With a supplement by Antoine Brunel
cites work: The limit of a renewal reward process with heavy-tailed rewards is not a linear fractional stable motion
cites work: Decomposition of self-similar stable mixed moving averages
cites work: Dilated fractional stable motions
cites work: On the structure of stationary stable processes
cites work: Q4247116
cites work: \((1/\alpha)\)-self similar \(\alpha\)-stable processes with stationary increments
cites work: Q4301585
cites work: Stable mixed moving averages
cites work: Integral-geometric construction of self-similar stable processes
DOI: 10.1214/AOP/1023481011
description: scientific article; zbMATH DE number 1906072