scholarly journals The Strong Laws of Large Numbers for Set-Valued Random Variables in Fuzzy Metric Space

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1192
Author(s):  
Li Guan ◽  
Juan Wei ◽  
Hui Min ◽  
Junfei Zhang
Keyword(s):  
Metric Space ◽  
Limit Theorems ◽  
Hausdorff Metric ◽  
Random Variables ◽  
Fuzzy Metric Space ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Fuzzy Metric ◽  
Large Numbers ◽  
Definition Of

In this paper, we firstly introduce the definition of the fuzzy metric of sets, and discuss the properties of fuzzy metric induced by the Hausdorff metric. Then we prove the limit theorems for set-valued random variables in fuzzy metric space; the convergence is about fuzzy metric induced by the Hausdorff metric. The work is an extension from the classical results for set-valued random variables to fuzzy metric space.

LAWS OF LARGE NUMBERS FOR WEIGHTED SUMS OF FUZZY SET-VALUED RANDOM VARIABLES

2004 ◽  
Vol 12 (06) ◽  
pp. 811-825 ◽  
Author(s):  
LI GUAN ◽  
SHOUMEI LI
Keyword(s):  
Fuzzy Set ◽  
Hausdorff Metric ◽  
Random Variables ◽  
Random Variable ◽  
Weighted Sums ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers

In this paper, we shall present weak and strong laws of large numbers (WLLN's and SLLN's) for weighted sums of independent (not necessarily identically distributed) fuzzy set-valued random variables in the sense of the extended Hausdorff metric [Formula: see text], based on the result of set-valued random variable obtained by Taylor and Inoue32,33. This work is a continuation of Li and Ogura20.

scholarly journals On Chung-Teicher type strong law for arrays of vector-valued random variables

2004 ◽  
Vol 2004 (9) ◽  
pp. 443-458
Author(s):  
Anna Kuczmaszewska
Keyword(s):  
Banach Space ◽  
Random Variables ◽  
Strong Law ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers ◽  
Random Elements ◽  
Vector Valued

We study the equivalence between the weak and strong laws of large numbers for arrays of row-wise independent random elements with values in a Banach spaceℬ. The conditions under which this equivalence holds are of the Chung or Chung-Teicher types. These conditions are expressed in terms of convergence of specific series ando(1)requirements on specific weighted row-wise sums. Moreover, there are not any conditions assumed on the geometry of the underlying Banach space.

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