Search Results

You are looking at 1 - 2 of 2 items for

• Author or Editor: Péter Kevei
• All content
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).

Restricted access

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.

Restricted access