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}
}
  • V. Pipiras, M. Taqqu
  • Published 5 May 2004
  • Mathematics
  • Annales De L Institut Henri Poincare-probabilites Et Statistiques
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… 
Mixed Moving Averages and Self-Similarity
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
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
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
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.

References

SHOWING 1-10 OF 16 REFERENCES
Integral representations of periodic and cyclic fractional stable motions
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
Decomposition of self-similar stable mixed moving averages
Abstract. Let α? (1,2) and Xα be a symmetric α-stable (S α S) process with stationary increments given by the mixed moving average where is a standard Lebesgue space, is some measurable function
Dilated Fractional Stable Motions
Dilated fractional stable motions are stable, self-similar, stationary increments random processes which are associated with dissipative flows. Self-similarity implies that their finite-dimensional
Stable stationary processes related to cyclic flows
We study stationary stable processes related to periodic and cyclic flows in the sense of Rosinski [Ann. Probab. 23 (1995) 1163–1187]. These processes are not ergodic. We provide their canonical
Structure of stationary stable processes
A connection between structural studies of stationary non-Gaussian stable processes and the ergodic theory of nonsingular flows is established and exploited. Using this connection, a unique
Processes with long-range correlations : theory and applications
Theory.- Prediction of Long-Memory Time Series: A Tutorial Review.- Fractional Brownian Motion and Fractional Gaussian Noise.- Scaling and Wavelets: An Introductory Walk.- Wavelet Estimation for the
MINIMAL INTEGRAL REPRESENTATIONS OF STABLE PROCESSES
Abstract: Minimal integral representations are defined for general st ochastic processes and completely characterized for stable processes ( symmetric and asymmetric). In the stable case, minimal
The structure of self-similar stable mixed moving averages
Let fi2 (1;2) and Xfi be a symmetric fi-stable (SfiS) process with stationary increments given by the mixed moving average Xfi(t) = Z
An introduction to infinite ergodic theory
Non-singular transformations General ergodic and spectral theorems Transformations with infinite invariant measures Markov maps Recurrent events and similarity of Markov shifts Inner functions
On the spectral representation of symmetric stable processes
...
1
2
...