研究生: |
呂冠見 Kuan-Chien Lu |
---|---|
論文名稱: |
一個對於模糊隨機變數的強大數法則和模糊馬亭戈的收斂定理 A Strong Laws of Large Numbers for Fuzzy Random Variables and Convergence Theorems for Martingales |
指導教授: | 王建都 |
學位類別: |
碩士 Master |
系所名稱: |
數學系 Department of Mathematics |
論文出版年: | 2002 |
畢業學年度: | 90 |
語文別: | 英文 |
論文頁數: | 40 |
中文關鍵詞: | 模糊集合; 、Hausdorff 距離 、模糊隨機變數的強大數法則 |
英文關鍵詞: | Fuzzy sets, Hausdorff metric, Strong law of large numbers for fuzzy random variables |
論文種類: | 學術論文 |
相關次數: | 點閱:318 下載:9 |
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對於可測函數在不同空間的大數法則,已經有被建構很多版本在文獻中.
在這篇論文中,我們證明了模糊隨機變數在一個非分離度量空間的大數法則 (沒有假設相同分配).此外我們也介紹模糊馬亭戈,模糊子馬亭戈,和模糊超馬亭戈.我們最後證明一些關於模糊子馬亭戈的收斂結果.
Many versions of the strong law of large
numbers have been established in the literature for measurable
functions taking values on different spaces. In this paper, we
prove a strong law of large numbers (it is not assumed to be
identically distributed) for fuzzy random variables on a
nonseparable metric space. Further, fuzzy martingales are
introduced, as well as fuzzy submartingales and supermartingales.
We prove some convergence results for fuzzy submartingales.
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