A Non-Uniform Estimate of the Rate of Convergence in the Central Limit Theorem for the Sums of Vector-Valued Functions of Independent Variables

1982 ◽  
Vol 26 (4) ◽  
pp. 773-786
Author(s):  
R. M. Gil’fanov
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Rate Of Convergence ◽  
Central Limit ◽  
Uniform Estimate ◽  
Independent Variables ◽  
The Central Limit Theorem ◽  
Vector Valued Functions ◽  
Vector Valued

scholarly journals A uniform estimate for the rate of convergence in the multidimensional central limit theorem for homogeneous Markov chains

1996 ◽  
Vol 19 (3) ◽  
pp. 441-450
Author(s):  
M. Gharib
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Rate Of Convergence ◽  
Central Limit ◽  
Remainder Term ◽  
Transition Probabilities ◽  
Uniform Estimate ◽  
Homogeneous Markov Chain ◽  
The Central Limit Theorem ◽  
Third Moment

In this paper a uniform estimate is obtained for the remainder term in the central limit theorem (CLT) for a sequence of random vectors forming a homogeneous Markov chain with arbitrary set of states. The result makes it possible to estimate the rate of convergence in the CLT without assuming the finiteness of the absolute third moment of the transition probabilities. Some consequences are also proved.

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