Law of the large numbers and probability inequalities for the independent random variables
| Autor: | Po-Chuan Yu, 游伯銓 |
|---|---|
| Rok vydání: | 1994 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 82 The techniques and the relative mathematical devices for proving the strong law of large numbers (S.L.L.N.) are studied in the thesis. We discuss how to slve the almost sure (a.s.) convergence problems of the sequence of partial sum. That is to deal with the S.L.L.N. The fundamental methods for proving the S.L.L.N. are surveyed in chapter 1. For understanding the application of the fundamental methods, the fundamental methods are used to prove Borel's S.L.L.N.By virtue of this study process, we will have a better and widespread understanding of the allied mathematical devicse for proving S.L.L.N. 4 fundamental methods for proving S.L.N.N. are collected and discussed. The extensive explorations on the mathematical devices of the above 4 fundamental methods are proposed in chapter 2. For better understanding method 1, we investigate the probability inequalities of partial sum. The curcial step in method 2 is to control the convergence of difference between convergent subsequence and original sequence. Method 3 has relation to the convergence of infinite series. The upper bounds of moment generating functions are explored when fundamental method 4 is used to prove S.S.L.N. the foregoing upper bounds have relation to the Gaussian random variable, so we study the application of the Gaussian random variable. The sufficent and necessary conditions of S.L.L.N. are surveyed in chapter 3 and 4 respectively. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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