正相协列乘积和的重对数律与强大数律

刘亦农;王岳宝

系统科学与数学 ›› 2006, Vol. 26 ›› Issue (5) : 609-618.

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PDF(299 KB)
系统科学与数学 ›› 2006, Vol. 26 ›› Issue (5) : 609-618. DOI: 10.12341/jssms08493
论文

正相协列乘积和的重对数律与强大数律

    刘亦农(1);王岳宝(2)
作者信息 +

The Law of Iterated Logarithm and Strong Law of Large Numbers for Product Sums of PA Sequences

    Liu Yinong(1);Wang Yuebao(2)
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文章历史 +

摘要

证明了强平稳正相协列乘积和的重对数律与不同分布正相协列乘积和的强大数律,指出了部分和服从强大数律但乘积和未必服从强大数律这一事实, 并讨论了定理2中一个条件的必要性.

Abstract

In this paper, the law of iterated logarithm for product sums of positive ssociated sequences with the strong stability and the strong law of large numbers for product sums of positive associated sequences with different distributions are proved. It is pointed out that the law of large numbers for product sums does not necessarily hold even though the law of large numbers for partial sums holds. Also the necessity of a condition in Theorem 2 is discussed.

关键词

正相协 / 乘积和 / 重对数律 / 强大数律

Key words

PA sequences / sums of product / the law of the iterated logarithm / the strong law of large numbers

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刘亦农 , 王岳宝. 正相协列乘积和的重对数律与强大数律. 系统科学与数学, 2006, 26(5): 609-618. https://doi.org/10.12341/jssms08493
Liu Yinong , Wang Yuebao. The Law of Iterated Logarithm and Strong Law of Large Numbers for Product Sums of PA Sequences. Journal of Systems Science and Mathematical Sciences, 2006, 26(5): 609-618 https://doi.org/10.12341/jssms08493
中图分类号: 60F15   
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