A Local Limit Theorem for Stationary Processes in the Domain of Attraction of a Normal Distribution

2001 ◽  
pp. 215-223 ◽  
Author(s):  
Jon Aaronson ◽  
Manfred Denker
Keyword(s):  
Limit Theorem ◽  
Normal Distribution ◽  
Local Limit Theorem ◽  
Domain Of Attraction ◽  
Local Limit ◽  
Stationary Processes

scholarly journals Central and Local Limit Theorems for Numbers of the Tribonacci Triangle

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 880
Author(s):  
Igoris Belovas
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Normal Distribution ◽  
Rate Of Convergence ◽  
Limit Theorems ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Constructive Proof ◽  
The Central Limit Theorem ◽  
Local Limit Theorems

In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of convergence to the limiting (normal) distribution, as well as a new proof of the local limit theorem for the numbers of the tribonacci triangle.

A LOCAL LIMIT THEOREM FOR CONTINUED FRACTIONS

2010 ◽  
Vol 10 (03) ◽  
pp. 429-439 ◽  
Author(s):  
ZBIGNIEW S. SZEWCZAK
Keyword(s):  
Limit Theorem ◽  
Continued Fractions ◽  
Limit Theorems ◽  
Continued Fraction ◽  
Local Limit Theorem ◽  
Domain Of Attraction ◽  
Local Limit ◽  
Continued Fraction Expansion ◽  
Normal Law

It is shown that functionals of digits in continued fraction expansion satisfy either the DeMoivre–Gnedenko or the Shepp–Stone limit theorems if and only if their marginals are in the domain of attraction of the normal law.

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