# Identification of periodic and cyclic fractional stable motions

@article{Pipiras2004IdentificationOP, title={Identification of periodic and cyclic fractional stable motions}, author={Vladas Pipiras and Murad S. Taqqu}, journal={Annales De L Institut Henri Poincare-probabilites Et Statistiques}, year={2004}, volume={44}, pages={612-637} }

Self-similar stable mixed moving average processes can be related to nonsingular flows through their minimal representations. Self-similar stable mixed moving averages related to dissipative flows have been studied, as well as processes associated with identity flows which are the simplest type of conservative flows. The focus here is on self-similar stable mixed moving averages related to periodic and cyclic flows. Periodic flows are conservative flows such that each point in the space comes…

## 4 Citations

Mixed Moving Averages and Self-Similarity

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- 2017

The focus of the chapter is on a large class of symmetric stable self-similar processes with stationary increments, known as self-similar mixed moving averages. Minimal representations of…

Integral representations of periodic and cyclic fractional stable motions

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- 2004

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…

SEMI-ADDITIVE FUNCTIONALS AND COCYCLES IN THE CONTEXT OF SELF-SIMILARITY

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Kernel functions of stable, self-similar mixed moving averages are known to be related to nonsingular flows. We identify and examine here a new functional occuring in this relation and study its…

Long-Range Dependence as a Phase Transition

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Long-range dependence in a stationary process has been understood as corresponding to a particular second-order behavior, to a particular range of the Hurst parameter, or of fractional integration.

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