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Chaotic behavior of infinitely divisible processes

S. Cambanis, K. Podgórski, A. Weron (1995)

Studia Mathematica

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.

Comparison between criteria leading to the weak invariance principle

Olivier Durieu, Dalibor Volný (2008)

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

The aim of this paper is to compare various criteria leading to the central limit theorem and the weak invariance principle. These criteria are the martingale-coboundary decomposition developed by Gordin in Dokl. Akad. Nauk SSSR188 (1969), the projective criterion introduced by Dedecker in Probab. Theory Related Fields110 (1998), which was subsequently improved by Dedecker and Rio in Ann. Inst. H. Poincaré Probab. Statist.36 (2000) and the condition introduced by Maxwell and Woodroofe in Ann. Probab.28...

Covariance structure of wide-sense Markov processes of order k ≥ 1

Arkadiusz Kasprzyk, Władysław Szczotka (2006)

Applicationes Mathematicae

A notion of a wide-sense Markov process X t of order k ≥ 1, X t W M ( k ) , is introduced as a direct generalization of Doob’s notion of wide-sense Markov process (of order k=1 in our terminology). A base for investigation of the covariance structure of X t is the k-dimensional process x t = ( X t - k + 1 , . . . , X t ) . The covariance structure of X t W M ( k ) is considered in the general case and in the periodic case. In the general case it is shown that X t W M ( k ) iff x t is a k-dimensional WM(1) process and iff the covariance function of x t has the triangular property....

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