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• Author or Editor: Péter Kevei
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Clear All Modify Search  # A note on asymptotics of linear combinations of iid random variables

Periodica Mathematica Hungarica
Author: Péter Kevei

## Abstract

Let X1,X2, ... be iid random variables, and let an = (a1,n, ..., an,n) be an arbitrary sequence of weights. We investigate the asymptotic distribution of the linear combination

\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} $$S_{a_n }$$ \end{document}
= a1,nX1 + ... + an,nXn under the natural negligibility condition limn→∞ max{|ak,n|: k = 1, ..., n} = 0. We prove that if
\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} $$S_{a_n }$$ \end{document}
is asymptotically normal for a weight sequence an, in which the components are of the same magnitude, then the common distribution belongs to
\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} $$\mathbb{D}$$ \end{document}
(2).

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# On the rate of convergence of the St. Petersburg game

Periodica Mathematica Hungarica
Authors: László Györfi and Péter Kevei

## Abstract

We investigate the repeated and sequential portfolio St. Petersburg games. For the repeated St. Petersburg game, we show an upper bound on the tail distribution, which implies a strong law for a truncation. Moreover, we consider the problem of limit distribution. For the sequential portfolio St. Petersburg game, we obtain tight asymptotic results for the growth rate of the game.

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