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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:304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.

    Abstract-----------------------------------1 1 Preliminaries and Notion-----------------2 1.1 Fuzzy set------------------------------8 1.2 Random compact set and Fuzzy Random 1.3 Support function----------------------22 2 A Strong of Large Numbers for Fuzzy Random-27 3 Convergence Theorem for fuzzy martingale--34 References---------------------------------39

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