A characterization and moving average representation for stable harmonizable processes.
Nikfar, M., Soltani, A.Reza (1996)
Journal of Applied Mathematics and Stochastic Analysis
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Nikfar, M., Soltani, A.Reza (1996)
Journal of Applied Mathematics and Stochastic Analysis
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Aleksander Weron (1993)
Studia Mathematica
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Gennady Samorodnitsky (2006)
Annales de la faculté des sciences de Toulouse Mathématiques
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This paper is a survey of both classical and new results and ideas on long memory, scaling and self-similarity, both in the light-tailed and heavy-tailed cases.
S. Cambanis, K. Podgórski, A. Weron (1995)
Studia Mathematica
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The hierarchy of chaotic properties of symmetric infinitely divisible stationary processes is studied in the language of their stochastic representation. The structure of the Musielak-Orlicz space in this representation is exploited here.
Soltani, A.R., Tarami, B. (2001)
Georgian Mathematical Journal
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A. Gross, A. Weron (1995)
Studia Mathematica
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In a 1987 paper, Cambanis, Hardin and Weron defined doubly stationary stable processes as those stable processes which have a spectral representation which is itself stationary, and they gave an example of a stationary symmetric stable process which they claimed was not doubly stationary. Here we show that their process actually had a moving average representation, and hence was doubly stationary. We also characterize doubly stationary processes in terms of measure-preserving regular...
Aleksander Janicki (1999)
Applicationes Mathematicae
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We present a method of numerical approximation for stochastic integrals involving α-stable Lévy motion as an integrator. Constructions of approximate sums are based on the Poissonian series representation of such random measures. The main result gives an estimate of the rate of convergence of finite-dimensional distributions of finite sums approximating such stochastic integrals. Stochastic integrals driven by such measures are of interest in constructions of models for various problems...
Cohen, Jason, Resnick, Sidney, Samorodnitsky, Gennady (1998)
Journal of Applied Mathematics and Stochastic Analysis
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Zbyněk Pawlas (2003)
Kybernetika
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Random measures derived from a stationary process of compact subsets of the Euclidean space are introduced and the corresponding central limit theorem is formulated. The result does not require the Poisson assumption on the process. Approximate confidence intervals for the intensity of the corresponding random measure are constructed in the case of fibre processes.