Mosco convergence of strong laws of large numbers for triangular array of row-wise exchangeable random sets and fuzzy random sets

Stochastics ◽  
2021 ◽  
pp. 1-25
Author(s):  
Nguyen Van Quang ◽  
Duong Xuan Giap
Keyword(s):  
Triangular Array ◽  
Mosco Convergence ◽  
Random Sets ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers ◽  
Fuzzy Random Sets ◽  
Fuzzy Random

Weak laws of large numbers for fuzzy random sets

2001 ◽  
Vol 47 (2) ◽  
pp. 1245-1256 ◽  
Author(s):  
Robert L. Taylor ◽  
Lynne Seymour ◽  
Yinpu Chen
Keyword(s):  
Random Sets ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Weak Laws ◽  
Fuzzy Random Sets ◽  
Fuzzy Random

scholarly journals Strong laws of large numbers for arrays of row-wise exchangeable random elements

1985 ◽  
Vol 8 (1) ◽  
pp. 135-144 ◽  
Author(s):  
Robert Lee Taylor ◽  
Ronald Frank Patterson
Keyword(s):  
Banach Space ◽  
Almost Sure Convergence ◽  
Kernel Density ◽  
Triangular Array ◽  
Density Estimates ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Kernel Density Estimates ◽  
Large Numbers ◽  
Random Elements

Let{Xnk,1≤k≤n,n≤1}be a triangular array of row-wise exchangeable random elements in a separable Banach space. The almost sure convergence ofn−1/p∑k=1nXnk,1≤p<2, is obtained under varying moment and distribution conditions on the random elements. In particular, strong laws of large numbers follow for triangular arrays of random elements in(Rademacher) typepseparable Banach spaces. Consistency of the kernel density estimates can be obtained in this setting.

A slln for arrays of rowwise exchangeable fuzzy random sets

1995 ◽  
Vol 13 (4) ◽  
pp. 461-470 ◽  
Author(s):  
Hiroshi Inoue ◽  
Robert L. Taylor
Keyword(s):  
Random Sets ◽  
Fuzzy Random Sets ◽  
Fuzzy Random
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