Convergence Theorems for Fuzzy Set-Valued Random Variables

2002 ◽  
pp. 191-219
Author(s):  
Shoumei Li ◽  
Yukio Ogura ◽  
Vladik Kreinovich
Keyword(s):  
Fuzzy Set ◽  
Random Variables ◽  
Convergence Theorems

A GENERAL METHOD FOR CONVERGENCE THEOREMS OF FUZZY SET-VALUED RANDOM VARIABLES AND ITS APPLICATIONS TO MARTINGALES AND UNIFORM AMARTS

2005 ◽  
Vol 13 (03) ◽  
pp. 243-253 ◽  
Author(s):  
SHOUMEI LI ◽  
JINPING ZHANG
Keyword(s):  
Fuzzy Set ◽  
Convergence Theorem ◽  
Hausdorff Metric ◽  
Random Variables ◽  
Convergence Result ◽  
Convergence Theorems ◽  
Sandwich Method ◽  
General Method

In this paper, we shall first give a general method for convergence theorem of fuzzy set-valued random variables. By using this "sandwich" method, we give the proofs of convergence theorems for fuzzy set-valued martingales, sub- and supermartingales in the sense of the extended Hausdorff metric H∞. Also we shall state a convergence result about uniform amarts.

scholarly journals Complete convergence and complete moment convergence for negatively dependent random variables under sub-linear expectations

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1093-1104
Author(s):  
Qunying Wu ◽  
Yuanying Jiang
Keyword(s):  
Probability Space ◽  
Complete Convergence ◽  
Random Variables ◽  
Complete Moment Convergence ◽  
Convergence Theorems ◽  
Dependent Random Variables ◽  
Moment Convergence ◽  
Negatively Dependent Random Variables

This paper we study and establish the complete convergence and complete moment convergence theorems under a sub-linear expectation space. As applications, the complete convergence and complete moment convergence for negatively dependent random variables with CV (exp (ln? |X|)) < ?, ? > 1 have been generalized to the sub-linear expectation space context. We extend some complete convergence and complete moment convergence theorems for the traditional probability space to the sub-linear expectation space. Our results generalize corresponding results obtained by Gut and Stadtm?ller (2011), Qiu and Chen (2014) and Wu and Jiang (2016). There is no report on the complete moment convergence under sub-linear expectation, and we provide the method to study this subject.

scholarly journals Some Types of Convergence for Negatively Dependent Random Variables under Sublinear Expectations

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Ruixue Wang ◽  
Qunying Wu
Keyword(s):  
Probability Space ◽  
Complete Convergence ◽  
Random Variables ◽  
Almost Sure Convergence ◽  
Weighted Sums ◽  
Convergence Theorems ◽  
Dependent Random Variables ◽  
Sublinear Expectation ◽  
Negatively Dependent Random Variables

In this paper, we research complete convergence and almost sure convergence under the sublinear expectations. As applications, we extend some complete and almost sure convergence theorems for weighted sums of negatively dependent random variables from the traditional probability space to the sublinear expectation space.

Strong laws of large numbers for independent fuzzy set-valued random variables

2006 ◽  
Vol 157 (19) ◽  
pp. 2569-2578 ◽  
Author(s):  
Shoumei Li ◽  
Yukio Ogura
Keyword(s):  
Fuzzy Set ◽  
Random Variables ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers
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