Limit theorems for randomly coarse grained continuous-time random walks
Agnieszka Jurlewicz
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Agnieszka Jurlewicz
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Czesław Stępniak (2015)
Discussiones Mathematicae Probability and Statistics
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Correlation coefficient is a well known measure of (linear) dependence between random variables. In his textbook published in 1980 L.T. Kubik introduced an analogue of such measure for random events A and B and studied its basic properties. We reveal that this measure reduces to the usual correlation coefficient between the indicator functions of A and B. In consequence the resuts by Kubik are obtained and strenghted directly. This is essential because the textbook is recommended by...
Pestana, Dinis (1981)
Portugaliae mathematica
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Z. Rychlik (1985)
Banach Center Publications
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J. Rosiński (1984)
Studia Mathematica
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F. Michel Dekking, Bram Kuijvenhoven (2011)
Journal of the European Mathematical Society
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Jan Rosiński
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CONTENTSI. Introduction.....................................................................................................................................................................5II. Preliminaries...................................................................................................................................................................7 1. Infinitely divisible probability measures on Banach spaces..........................................................................................7 2....
Jan Rosiński, Wojbor A. Woyczyński (1987)
Colloquium Mathematicae
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Marta Borowiecka-Olszewska, Jolanta K. Misiewicz (2003)
Discussiones Mathematicae Probability and Statistics
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In this paper, we consider a symmetric α-stable p-sub-stable two-dimensional random vector. Our purpose is to show when the function 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].
Malishić, J. (1986)
Publications de l'Institut Mathématique. Nouvelle Série
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Kifer, Yuri (1998)
Documenta Mathematica
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Eugene Wong, Moshe Zakai (1989)
Séminaire de probabilités de Strasbourg
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Brockett, Patrick L. (1978)
International Journal of Mathematics and Mathematical Sciences
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W. Dziubdziela (1976)
Applicationes Mathematicae
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François Germinet (2007-2008)
Séminaire Équations aux dérivées partielles
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In this review, we first recall a recent Bernoulli decomposition of any given non trivial real random variable. While our main motivation is a proof of universal occurence of Anderson localization in continuum random Schrödinger operators, we review other applications like Sperner theory of antichains, anticoncentration bounds of some functions of random variables, as well as singularity of random matrices.
Nicolay N. Demesh, Sergey L. Chekhmenok (2005)
SORT
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In earlier papers, 2π-periodic spectral data windows have been used in spectral estimation of discrete- time random fields having finite second-order moments. In this paper, we show that 2π-periodic spectral windows can also be used to construct estimates of the spectral density of a homogeneous symmetric α-stable discrete-time random field. These fields do not have second-order moments if 0 < α < 2. We construct an estimate of the spectrum, calculate the asymptotic mean...