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Universally typical sets for ergodic sources of multidimensional data

Tyll Krüger, Guido F. Montúfar, Ruedi Seiler, Rainer Siegmund-Schultze (2013)

Kybernetika

We lift important results about universally typical sets, typically sampled sets, and empirical entropy estimation in the theory of samplings of discrete ergodic information sources from the usual one-dimensional discrete-time setting to a multidimensional lattice setting. We use techniques of packings and coverings with multidimensional windows to construct sequences of multidimensional array sets which in the limit build the generated samples of any ergodic source of entropy rate below an $h_{0}$ with...

Valeurs extrémales d'échantillons croissants d'une variable aléatoire réelle

Paul Deheuvels (1974)

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

Various limit theorems for ratios from the uniform distribution

Yu Miao, Yan Sun, Rujun Wang, Manru Dong (2016)

Open Mathematics

In this paper, we consider the ratios of order statistics in samples from uniform distribution and establish strong and weak laws for these ratios.

Velocity and Lyapounov exponents of some random walks in random environment

Martin P. W. Zerner (2000)

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

Vitesse de fuite et comportement asymptotique du mouvement brownien sur les groupes nilpotents

L. Gallardo (1981)

Annales scientifiques de l'Université de Clermont. Mathématiques

Wavelets, Generalized White Noise and Fractional Integration: The Synthesis of Fractional Brownian Motion.

Y. Meyer, F. Sellan, M.S. Taqqu (1999)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

Weak convergence of mutually independent $X ₙ^{B}$ and $X ₙ^{A}$ under weak convergence of $X ₙ \equiv X ₙ^{B} - X ₙ^{A}$

W. Szczotka (2006)

Applicationes Mathematicae

For each n ≥ 1, let $v_{n, k}, k \geq 1$ and $u_{n, k}, k \geq 1$ be mutually independent sequences of nonnegative random variables and let each of them consist of mutually independent and identically distributed random variables with means v̅ₙ and u̅̅ₙ, respectively. Let $X ₙ^{B} (t) = (1 / c ₙ) \sum_{j = 1}^{[n t]} (v_{n, j} - v ̅ ₙ)$ , $X ₙ^{A} (t) = (1 / c ₙ) \sum_{j = 1}^{[n t]} (u_{n, j} - u ̅ ̅ ₙ)$ , t ≥ 0, and $X ₙ = X ₙ^{B} - X ₙ^{A}$ . The main result gives conditions under which the weak convergence $X ₙ \overset{}{\to} X$ , where X is a Lévy process, implies $X ₙ^{B} \overset{}{\to} X^{B}$ and $X ₙ^{A} \overset{}{\to} X^{A}$ , where $X^{B}$ and $X^{A}$ are mutually independent Lévy processes and $X = X^{B} - X^{A}$ .