A note on the almost sure central limit theorem for the product of partial sums of m-dependent random variables

2018 ◽  
Vol 48 (9) ◽  
pp. 2102-2112
Author(s):  
Yu Miao ◽  
Xiaoyan Xu
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Variables ◽  
Partial Sums ◽  
Dependent Random Variables

scholarly journals An expansion related to the central limit theorem

1969 ◽  
Vol 10 (1-2) ◽  
pp. 219-230
Author(s):  
C. R. Heathcote
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Variables ◽  
Partial Sums ◽  
The Central Limit Theorem ◽  
Independent And Identically Distributed

Let X1, X2,…be independent and identically distributed non-lattice random variables with zero, varianceσ2<∞, and partial sums Sn = X1+X2+…+X.

scholarly journals On Feller's criterion for the law of the iterated logarithm

1994 ◽  
Vol 17 (2) ◽  
pp. 323-340 ◽  
Author(s):  
Deli Li ◽  
M. Bhaskara Rao ◽  
Xiangchen Wang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Uniform Estimate ◽  
Random Variables ◽  
Independent Random Variables ◽  
Partial Sums ◽  
The Central Limit Theorem ◽  
Iterated Logarithm ◽  
The Law

Combining Feller's criterion with a non-uniform estimate result in the context of the Central Limit Theorem for partial sums of independent random variables, we obtain several results on the Law of the Iterated Logarithm. Two of these results refine corresponding results of Wittmann (1985) and Egorov (1971). In addition, these results are compared with the corresponding results of Teicher (1974), Tomkins (1983) and Tomkins (1990)

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