i.i.d随机变量部分和最大值序列的强大数定律

IF 0.4 4区数学 Q4 STATISTICS & PROBABILITY

Probability and Mathematical Statistics-Poland Pub Date : 2019-06-10 DOI:10.19195/0208-4147.39.1.2

Shuhua Chang, Deli Li, A. Rosalsky

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引用次数: 0

摘要

设0 < p≤2，设{Xn;n≥1}为实值随机变量X的独立副本序列，设Sn = X1 +…+ Xn, n≥- 1。本文从Mikosch 1984的一个定理出发，建立了数列{max1≤k≤n |Sk|;N≥- 1}。更具体地说，给出了limn→∞max1≤k≤n |Sk|log n−1 = e1/p a.s，其中log x = loge max{e, x}， x≥- 0的充要条件。

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Strong laws of large numbers for the sequence of the maximum of partial sums of i.i.d. random variables

Let 0 < p ≤ 2, let {Xn; n ≥ 1} be a sequence of independent copies of a real-valued random variable X, and set Sn = X1 + . . . + Xn, n ≥ 1. Motivated by a theorem of Mikosch 1984, this note is devoted to establishing a strong law of large numbers for the sequence {max1≤k≤n |Sk| ; n ≥ 1}. More specifically, necessary and sufficient conditions are given forlimn→∞ max1≤k≤n |Sk|log n−1 = e1/p a.s.,where log x = loge max{e, x}, x ≥ 0.

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来源期刊

Probability and Mathematical Statistics-Poland STATISTICS & PROBABILITY-

CiteScore

0.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： PROBABILITY AND MATHEMATICAL STATISTICS is published by the Kazimierz Urbanik Center for Probability and Mathematical Statistics, and is sponsored jointly by the Faculty of Mathematics and Computer Science of University of Wrocław and the Faculty of Pure and Applied Mathematics of Wrocław University of Science and Technology. The purpose of the journal is to publish original contributions to the theory of probability and mathematical statistics.