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About the density of spectral measure of the two-dimensional SaS random vector

100%
Borowiecka-Olszewska M., Misiewicz J.
Discussiones Mathematicae Probability and Statistics
|
2003
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tom 23
|
nr 1
77-81
EN
In this paper, we consider a symmetric α-stable p-sub-stable two-dimensional random vector. Our purpose is to show when the function $exp{-(|a|p + |b|p)^{α/p}}$ is a characteristic function of such a vector for some p and α. The solution of this problem we can find in [3], in the language of isometric embeddings of Banach spaces. Our proof is based on simple properties of stable distributions and some characterization given in [4].
2
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Semi-additive functionals and cocycles in the context of self-similarity

75%
Pipiras V., Taqqu M.
Discussiones Mathematicae Probability and Statistics
|
2010
|
tom 30
|
nr 2
149-177
EN
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 properties. To prove its existence, we develop a general result about semi-additive functionals related to cocycles. The functional we identify, is helpful when solving for the kernel function generated by a flow. Its presence also sheds light on the previous results on the subject.
3
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Positive stable realizations of fractional continuous-time linear systems

75%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2011
|
tom 21
|
nr 4
697-702
EN
Conditions for the existence of positive stable realizations with system Metzler matrices for fractional continuous-time linear systems are established. A procedure based on the Gilbert method for computation of positive stable realizations of proper transfer matrices is proposed. It is shown that linear minimum-phase systems with real negative poles and zeros always have positive stable realizations.
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