Displaying similar documents to “Approximation of L 2 -processes by Gaussian processes.”

Chaotic behavior of infinitely divisible processes

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.

Weakly mixing but not mixing quasi-Markovian processes

Zbigniew Kowalski (2000)

Studia Mathematica

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Let (f,α) be the process given by an endomorphism f and by a finite partition α = A i i = 1 s of a Lebesgue space. Let E(f,α) be the class of densities of absolutely continuous invariant measures for skew products with the base (f,α). We say that (f,α) is quasi-Markovian if E ( f , α ) ⊂ g : ⋁ B i i = 1 s s u p p g = ⋃ i = 1 s A i × B i . We show that there exists a quasi-Markovian process which is weakly mixing but not mixing. As a by-product we deduce that the set of all coboundaries which are measurable with respect to the ’chequer-wise’ partition for σ ×...

Spontaneous clustering in theoretical and some empirical stationary processes

T. Downarowicz, Y. Lacroix, D. Léandri (2010)

ESAIM: Probability and Statistics

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In a stationary ergodic process, clustering is defined as the tendency of events to appear in series of increased frequency separated by longer breaks. Such behavior, contradicting the theoretical “unbiased behavior” with exponential distribution of the gaps between appearances, is commonly observed in experimental processes and often difficult to explain. In the last section we relate one such empirical example of clustering, in the area of marine technology. In the theoretical part...

Limit theory for some positive stationary processes with infinite mean

Jon Aaronson, Roland Zweimüller (2014)

Annales de l'I.H.P. Probabilités et statistiques

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We prove stable limit theorems and one-sided laws of the iterated logarithm for a class of positive, mixing, stationary, stochastic processes which contains those obtained from nonintegrable observables over certain piecewise expanding maps. This is done by extending Darling–Kac theory to a suitable family of infinite measure preserving transformations.