scholarly journals Strong Renewal Theorem and Local Limit Theorem in the Absence of Regular Variation

2021 ◽  
Author(s):  
Péter Kevei ◽  
Dalia Terhesiu
Keyword(s):  
Limit Theorem ◽  
Regular Variation ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Renewal Theorem ◽  
Strong Renewal Theorem

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.

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