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

呂冠見(Kuan-Chien Lu)

指導教授 ： 王建都

國立臺灣師範大學/理學院/數學系/碩士(2001年)

摘要

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.

關鍵字

模糊集合 ； Hausdorff 距離 ； 模糊隨機變數的強大數法則

並列摘要

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.

並列關鍵字

Fuzzy sets ； Hausdorff metric ； Strong law of large numbers for fuzzy random variables

參考文獻

N.S. Papageorgiou, On the Theory of Banach space valued

[19] G. Krupa, Convergence

of unbounded multivalued supermartingales in the Mosco and Slice

[2] R.J. Aumann, Integrals of set-valued functions, J. Math. Anal. Appl. 12 (1965) 1-12.

[3] Z. Artstein, and R. A. Vitale, A strong law of large