Open Access
2007 Integral representations of periodic and cyclic fractional stable motions
Vladas Pipiras, Murad Taqqu
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Electron. J. Probab. 12: 181-206 (2007). DOI: 10.1214/EJP.v12-395


Stable non-Gaussian self-similar mixed moving averages can be decomposed into several components. Two of these are the periodic and cyclic fractional stable motions which are the subject of this study. We focus on the structure of their integral representations and show that the periodic fractional stable motions have, in fact, a canonical representation. We study several examples and discuss questions of uniqueness, namely how to determine whether two given integral representations of periodic or cyclic fractional stable motions give rise to the same process.


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Vladas Pipiras. Murad Taqqu. "Integral representations of periodic and cyclic fractional stable motions." Electron. J. Probab. 12 181 - 206, 2007.


Accepted: 27 February 2007; Published: 2007
First available in Project Euclid: 1 June 2016

zbMATH: 1130.60048
MathSciNet: MR2299916
Digital Object Identifier: 10.1214/EJP.v12-395

Primary: 60G18 , 60G52
Secondary: 28D , 37A

Keywords: cocycles , Mixed moving averages , Periodic and cyclic flows , Self-similar processes with stationary increments , semi-additive functionals , Stable

Vol.12 • 2007
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