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The aim of the paper is to establish strong laws of large numbers for sequences of blockwise and pairwise $m$ -dependent random variables in a convex combination space with or without compactly uniformly integrable condition. Some of our results are even new in the case of real random variables.

Strong laws of large numbers for $𝔹$ -valued random fields.

Lagodowski, Zbigniew A. (2009)

Discrete Dynamics in Nature and Society

Strong laws of large numbers for weighted sums of random elements in normed linear spaces.

Adler, Andre, Rosalsky, Andrew, Taylor, Robert L. (1989)

International Journal of Mathematics and Mathematical Sciences

Strong laws of large numbers in certain linear spaces

Wojbor A. Woyczynski (1974)

Annales de l'institut Fourier

In this paper we are concerned with the norm almost sure convergence of series of random vectors taking values in some linear metric spaces and strong laws of large numbers for sequences of such random vectors. Section 2 treats the Banach space case where the results depend upon the geometry of the unit cell. Section 3 deals with spaces equipped with a non-necessarily homogeneous $F$ -norm and in Section 4 we restrict our attention to sequences of identically distributed random vectors.

Strong tightness as a condition of weak and almost sure convergence

Grzegorz Krupa, Wiesław Zieba (1996)

Commentationes Mathematicae Universitatis Carolinae

A sequence of random elements ${X_{j}, j \in J}$ is called strongly tight if for an arbitrary $ϵ > 0$ there exists a compact set $K$ such that $P (⋂_{j \in J} [X_{j} \in K]) > 1 - ϵ$ . For the Polish space valued sequences of random elements we show that almost sure convergence of ${X_{n}}$ as well as weak convergence of randomly indexed sequence ${X_{τ}}$ assure strong tightness of ${X_{n}, n \in ℕ}$ . For $L^{1}$ bounded Banach space valued asymptotic martingales strong tightness also turns out to the sufficient condition of convergence. A sequence of r.e. ${X_{n}, n \in ℕ}$ is said to converge essentially with...

Structural relation

Václav Fabian (1954)

Czechoslovak Mathematical Journal

Substable and pseudo-isotropic processes. Connections with the geometry of subspaces of $L_{α}$ [Book]

Misiewicz Jolanta K. (1996)

Sulla assoluta continuità di una variabile aleatoria la cui densità è limite di una successione di densità costanti a tratti

Mario Volpato, Alberto Bressan (1978)

Rendiconti del Seminario Matematico della Università di Padova

Summability of double independent random variables.

Patterson, Richard F., Savaş, Ekrem (2008)

Journal of Inequalities and Applications [electronic only]

Sums of independent Banach space valued random variables

Jørgen Hoffmann-Jørgensen (1974)

Studia Mathematica

Sums of independent Banach space valued random variables (after J. Hoffmann-Jørgensen)

S. Kwapien (1972/1973)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

Sums of powers: an arithmetic refinement to the probabilistic model of Erdős and Rényi

Jean-Marc Deshouillers, François Hennecart, Bernard Landreau (1998)

Acta Arithmetica

Erdős and Rényi proposed in 1960 a probabilistic model for sums of s integral sth powers. Their model leads almost surely to a positive density for sums of s pseudo sth powers, which does not reflect the case of sums of two squares. We refine their model by adding arithmetical considerations and show that our model is in accordance with a zero density for sums of two pseudo-squares and a positive density for sums of s pseudo sth powers when s ≥ 3. Moreover, our approach supports a conjecture of...

Supporteurs des prodistributions et mesures cylindriques

Walter Schachermayer (1974/1975)

Séminaire Paul Krée

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Displaying 61 – 80 of 112

Substable and pseudo-isotropic processes. Connections with the geometry of subspaces of L α [Book]

Currently displaying 61 – 80 of 112

Substable and pseudo-isotropic processes. Connections with the geometry of subspaces of $L_{α}$ [Book]