臺灣博碩士論文加值系統

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。

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.

第一章:導論..................p.3
第二章:主要內容..............p.7
第三章:應用與過去文獻之比較...p.14

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.

5. Etmadi, N. (1981), An elementary proof of the strong law of large numbers, Z. Wahrscheinlichkeitstheor und verw. Geb. 55, 119-122.

6. Kolmogorov, A. (1933), Grundbegriffe der wahrscheinlichkeisrechnung, Springer-Verlag, Berlin.

7. Liu, L. (2009), Precise large deviations for depandent random variables with heavy tail, Statistics and Probability Letters, 79, 1290-1298.

8. Shen, A. (2011), Probability inequslities for END sequence and their applications, Journal of Inequalities and Applications, 2011:98.

9. Tang, X., (2013), Some strong laws of large numbers for weighted sums of asymptotically almost negatively associated random variables, Journal of Inequalities and Applications, 2013:4.

10. Yuan, D.M. and An ,J. (2009), Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications. Sci. China (Ser. A): Mathematices 52, 9, 1887-1904.

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.