正随机变量的大数定律

IF 0.6 Q3 MATHEMATICS

Illinois Journal of Mathematics Pub Date : 2021-11-30 DOI:10.1215/00192082-10817817

I. Karatzas, W. Schachermayer

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引用次数: 1

摘要

根据著名的KOML（1967）定理的精神，概率空间上的每一个非负可测函数$\｛f_n｝_｛n\In\n｝$序列都包含一个子序列，该子序列及其所有子序列收敛，例如，在CES中，ARO均值为某个可测$f_*：\ Omega \ to[0，\ infty]$。本文用一种新的方法和初等工具证明了VON WEIZS“ACKER（2004）的这一结果，这些方法和工具也强化了DELBAEN和SCHACHERMAYER（1994）的一个定理，用CES“ARO均值代替了一般的凸组合。

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A strong law of large numbers for positive random variables

In the spirit of the famous KOML\'OS (1967) theorem, every sequence of nonnegative, measurable functions $\{ f_n \}_{n \in \N}$ on a probability space, contains a subsequence which - along with all its subsequences - converges a.e. in CES\`ARO mean to some measurable $f_* : \Omega \to [0, \infty]$. This result of VON WEIZS\"ACKER (2004) is proved here using a new methodology and elementary tools; these sharpen also a theorem of DELBAEN&SCHACHERMAYER (1994), replacing general convex combinations by CES\`ARO means.

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来源期刊

Illinois Journal of Mathematics 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

期刊介绍： IJM strives to publish high quality research papers in all areas of mainstream mathematics that are of interest to a substantial number of its readers. IJM is published by Duke University Press on behalf of the Department of Mathematics at the University of Illinois at Urbana-Champaign.