The strong law of large numbers for sums of randomly chosen random variables

被引：1

作者：

Gdula, Agnieszka M. ^{[1
]}

Krajka, Andrzej ^{[1
]}

机构：

[1] Marie Curie Sklodowska Univ, Ul Akad 9, PL-20033 Lublin, Poland

来源：

LITHUANIAN MATHEMATICAL JOURNAL | 2021年 / 61卷 / 04期

关键词：

strong law of large numbers; randomly indexed sums; random sets;

D O I：

10.1007/s10986-021-09528-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let {X(n,)n >= 1} be a sequence of independent or identically distributed dependent random variables, and let {A(n,)n >= 1} be a sequence of random subsets of natural numbers independent of {X-n, n >= 1}. In this paper, we describe the strong law of large numbers (SLLN) of the form Sigma(i is an element of An)(X-i - E Sigma(i is an element of An) X-i)/b(n) -> 0 a.s. as n -> infinity for some sequence of nondecreasing positive numbers {b(n), n >= 1}. There often arises an assumption that {A(n), n >= 1} are almost surely increasing: A(n) subset of A(n + 1), a. s n >= 1.

引用

页码：471 / 482

页数：12