強大數法則之研究

A Study on Strong Law of Large numbers

張閎鈞(Zhang, Hong Jun)

指導教授 ： 胡殿中

國立清華大學/理學院/數學系/碩士(2016年)

摘要

在本文中,我們將討論一般隨機變數數列在滿足某些動差條件下,會有傳統強大數法則的結果。在第一章中,我們將討論前人在隨機變數數列具有特殊結構下的成果,我們主要討論的特殊結構有:pairwise independent、extended negatively dependent(END)、asymptotically almost negatively associated(AANA)。在第二章中,我們將給出本文的主要結果和證明。在第三章中,我們將討論當隨機變數數列具有在第一章提及的特殊結構時,如何利用我們的結果而得到傳統強大數法則。

關鍵字

強大數法則

並列摘要

In this paper, we study a general sequence of random variables under some moment conditions will follow the classical strong law of large numbers. In Chapter 1, we discuss the results of previous studies in in the sequence with special structures. These special structures contain independent, pairwise independent, extended negatively dependent (END), and asymptotically almost negatively associated (AANA). In Capter 2, we give our main results and prove. In Chapter 3, we show that how to use our main results to obtain classical strong law of large numbers when the sequence has special structures referred to Chapter 1.

並列關鍵字

strong law of large numbers

參考文獻

11. 王國龍 (2014), 關於廣義負相依隨機變數的極限理論之研究, 國立清華大學博士論文.

1. Chandra, T.K. and Ghosal, S. (1996), Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables, Acta Math. Hungar, 71, 327-336.

2. Chen, P., Bai, P. and Sung, S.H. (2014) The von Bahr-Esseen moment inequality for pairwise independent random variables and appliciation, J. Math. Anal. Appl. 419 1290-1302.

3. Chen, Y., Chen, A. Chen and Kai W. Ng (2010), The strong law of large numbers for extended negatively dependent random variables, J. Appl Prob. 47, 908-922.

4.Csorgo, S., Tandori, K. and Totik, V. (1983), On the strong law of large numbers for pairwise indepent random variables, Acta Math. Hungar, 42, 319-330.