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Integral representations of periodic and cyclic fractional stable motions. (English) Zbl 1130.60048
Summary: 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.

MSC:
60G18 Self-similar stochastic processes
60G52 Stable stochastic processes
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