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研究生:呂冠見
研究生(外文):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
論文名稱(外文):A Strong Laws of Large Numbers for Fuzzy Random Variables and Convergence Theorems for Martingales
指導教授:王建都王建都引用關係
學位類別:碩士
校院名稱:國立臺灣師範大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
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
外文關鍵詞:Fuzzy setsHausdorff metricStrong law of large numbers for fuzzy random variables
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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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