On Necessary Conditions of Probability Limit Theorems in Finite Algebras

2020 ◽  
Vol 102 (1) ◽  
pp. 301-303
Author(s):  
A. D. Yashunsky
Keyword(s):  
Limit Theorems ◽  
Necessary Conditions ◽  
Probability Limit ◽  
Finite Algebras

scholarly journals Non-commutative probability limit theorems

1984 ◽  
Vol 78 (1) ◽  
pp. 59-75 ◽  
Author(s):  
K. Urbanik
Keyword(s):  
Limit Theorems ◽  
Probability Limit

Some probability limit theorems with statistical applications

1953 ◽  
Vol 49 (2) ◽  
pp. 239-246 ◽  
Author(s):  
P. H. Diananda ◽  
M. S. Bartlett
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Upper Bounds ◽  
Central Limit Theorems ◽  
Conditional Distributions ◽  
Probability Limit ◽  
Direct Generalization ◽  
Dependent Variables ◽  
Linear Scalar

In fundamental papers Bernstein (3) and Loève(8) have proved central limit theorems for wide classes of dependent variables. Their theorems are stated in terms of conditional distributions. In the case of dn-dependent variables (see § 3) they assume the existence, as the ‘conditioning’ variates vary, of finite upper bounds for certain conditional absolute moments higher than the second. More recently, Hoeffding and Robbins (7) have proved central limit theorems for m-dependent variables with finite third absolute moments, and Moran(10) has given a direct generalization of the Lindeberg-Lévy theorem for stationary discrete linear scalar processes.

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