# Search Results

## You are looking at 1 - 10 of 35 items for :

• "law of large numbers"
• All content
Clear All

# Strong laws of large numbers in von Neumann algebras

Acta Mathematica Hungarica
Author: Katarzyna Klimczak

References [1] Batty , C. J. K. 1979 The strong law of large numbers for states and traces of a W*-algebra Z. Wahrsch. Verw

Restricted access

# On the strong law of large numbers for ϕ-mixing and ρ-mixing random variables

Acta Mathematica Hungarica
Author: Anna Kuczmaszewska

. Probab. Lett. 79 105 – 111 10.1016/j.spl.2008.07.026 . [3] Fazekas , I. , Klesov , O. 2000 A general approach to the strong laws of large numbers Teor. Verojatnost. i Primenen. 45 569

Restricted access

# Fulfilment of the law of large numbers in case of variance determinations

Acta Geodaetica et Geophysica Hungarica
Authors: B. Hajagos and Ferenc Steiner

As the variance (the square of the minimum L 2-norm, i.e., the square of the scatter) is one of the basic characteristics of the conventional statistics, it is of practical importance to know the errors of its determination for different parent distribution types. This statement is outstandingly valid for the geostatistics because the (h) variogram (called also as semi-variogram) is defined as the half variance of some quantity-difference (e.g. difference of ore concentrations) in function of the h dis- tance of the measuring points and this g (h)-curve plays a basic role in the classical geostatistics. If the scatter (s VAR) is chosen to characterize the determination uncertainties of the variance (denoted the latter by VAR), this can be easily calculate as the quotient A VAR= Ön (if the number n of the elements in the sample is large enough); for the so-called asymptotic scatter A VAR is known a simple formula (containing the fourth moment). The present paper shows that the AVAR has finite value unfortunately only for about a quarter of distribution types occurring in the earth sciences, it must be especially accentuate that A VAR has infinite value for that distribution type which most frequent occurs in the geostatistics. It is proven by the present paper that the law of large numbers is always fulfilled (i.e., the error always decreases if n increases) for the error-determinations if the semi-intersextile range is accepted (instead of the scatter); the single (quite natural) condition is the existence of the theoretical variance for the parent distribution. __

Restricted access

# On the strong laws of large numbers for double arrays of random variables in convex combination spaces

Acta Mathematica Hungarica
Authors: Nguyen Van Quang and Nguyen Tran Thuan

On the strong law of large numbers for pairwise independent random variables Acta Math. Hungar. 42 319 – 330 10.1007/BF01956779 . [3

Restricted access

# Strong laws of large numbers for random forests

Acta Mathematica Hungarica
Authors: A. Chuprunov and I. Fazekas

## Abstract

Random forests are studied. A moment inequality and a strong law of large numbers are obtained for the number of trees having a fixed number of nonroot vertices.

Restricted access

# Inequalities and strong laws of large numbers for random allocations

Acta Mathematica Hungarica
Authors: Alexey Chuprunov and István Fazekas

Moment inqualities and strong laws of large numbers are proved for random allocations of balls into boxes. Random broken lines and random step lines are constructed using partial sums of i.i.d. random variables that are modified by random allocations. Functional limit theorems for such random processes are obtained.

Restricted access

# Laws of large numbers for cooperative St. Petersburg gamblers

Periodica Mathematica Hungarica
Authors: Sándor Csörgő and Gordon Simons

Summary General linear combinations of independent winnings in generalized \St~Petersburg games are interpreted as individual gains that result from pooling strategies of different cooperative players. A weak law of large numbers is proved for all such combinations, along with some almost sure results for the smallest and largest accumulation points, and a considerable body of earlier literature is fitted into this cooperative framework. Corresponding weak laws are also established, both conditionally and unconditionally, for random pooling strategies.

Restricted access

# On the strong law of large numbers and additive functions

Periodica Mathematica Hungarica
Authors: István Berkes, Wolfgang Müller, and Michel Weber

## Abstract

Let f(n) be a strongly additive complex-valued arithmetic function. Under mild conditions on f, we prove the following weighted strong law of large numbers: if X,X 1,X 2, … is any sequence of integrable i.i.d. random variables, then

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathop {\lim }\limits_{N \to \infty } \frac{{\sum\nolimits_{n = 1}^N {f(n)X_n } }} {{\sum\nolimits_{n = 1}^N {f(n)} }} = \mathbb{E}Xa.s.$$ \end{document}

Restricted access

# Weak laws of large numbers for cooperative gamblers

Periodica Mathematica Hungarica
Authors: Sándor Csörgő and Gordon Simons

## Abstract

Based on a stochastic extension of Karamata’s theory of slowly varying functions, necessary and sufficient conditions are established for weak laws of large numbers for arbitrary linear combinations of independent and identically distributed nonnegative random variables. The class of applicable distributions, herein described, extends beyond that for sample means, but even for sample means our theory offers new results concerning the characterization of explicit norming sequences. The general form of the latter characterization for linear combinations also yields a surprising new result in the theory of slow variation.

Restricted access

# One-sided strong laws forincrements of sumsof i.i.d. random variables

Studia Scientiarum Mathematicarum Hungarica
Author: A. N. Frolov

ERDŐS, P. and RÉNYI, A., On a new law of large numbers, J. Analyse Math. 23 (1970), 103-111. MR 42 # 6907 On a new law of large numbers J. Analyse Math

Restricted access