On a Non-Uniform Estimate for the Rate of Convergence in a Local Limit Theorem for a Stable Limit Distribution

1983 ◽  
Vol 27 (3) ◽  
pp. 607-609 ◽  
Author(s):  
A. S. Mal’kov ◽  
V. V. Ul’yanov
Keyword(s):  
Limit Theorem ◽  
Rate Of Convergence ◽  
Limit Distribution ◽  
Local Limit Theorem ◽  
Uniform Estimate ◽  
Local Limit ◽  
Stable Limit ◽  
Stable Limit Distribution

scholarly journals The local limit theorem for sums of random variables defined on a homogeneous Markov chain in the case of the stable limit distribution law

1961 ◽  
Vol 1 (1-2) ◽  
pp. 7-16
Author(s):  
A. Aleškevičienė
Keyword(s):  
Markov Chain ◽  
Limit Theorem ◽  
Limit Distribution ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Homogeneous Markov Chain ◽  
Stable Limit ◽  
Distribution Law ◽  
Sums Of Random Variables ◽  
Stable Limit Distribution

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: A. Алешкявичене. Локальная предельная теорема для сумм случайных величин, связанных в однородную цепь Маркова в случае устойчивого предельного распределения A. Aleškevičienė. Lokalinė ribinė teorema atsitiktinių dydžių, surištų homogenine Markovo grandine, sumoms stabilaus ribinio dėsnio atveju  

scholarly journals The multi-dimensional local limit theorem for the Markov chain in the case of the stable limit distribution law

1962 ◽  
Vol 2 (1) ◽  
pp. 6-8
Author(s):  
A. Aleškevičienė
Keyword(s):  
Markov Chain ◽  
Limit Theorem ◽  
Limit Distribution ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Stable Limit ◽  
Distribution Law ◽  
Stable Limit Distribution

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: А. Алешкявичене, Многомерная локальная предельная теорема для однородной цепи Маркова в случае устойчивого предельного закона A. Aleškevičienė, Daugiamatė lokalinė ribinė teorema homogeninei Markovo grandinei stabilaus ribinio dėsnio atveju

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 non-uniform rate of convergence in a local limit theorem

1978 ◽  
Vol 84 (2) ◽  
pp. 351-359 ◽  
Author(s):  
Sujit K. Basu
Keyword(s):  
Limit Theorem ◽  
Rate Of Convergence ◽  
Local Limit Theorem ◽  
Random Variables ◽  
Local Limit ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Standard Normal ◽  
The Common ◽  
Necessary And Sufficient

AbstractLet {Xn} be a sequence of iid random variables. If the common charac-teristic function is absolutely integrable in mth power for some integer m ≥ 1, then Zn = n−½(X1 + … + Xn) has a pdf fn for all n ≥ m. Here we give a necessary and sufficient condition for sup as n. → ∞, where φ (x) is the standard normal pdf and M(x) is a non-decreasing function of x ≥ 0 such that M(0) > 0 and M(x)/xδ is non-increasing for 0 < δ ≤ 1.

On the rate of convergence in a local limit theorem

1974 ◽  
Vol 76 (1) ◽  
pp. 307-312 ◽  
Author(s):  
Sujit K. Basu
Keyword(s):  
Distribution Function ◽  
Limit Theorem ◽  
Probability Density Function ◽  
Characteristic Function ◽  
Rate Of Convergence ◽  
Inversion Formula ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Common Distribution ◽  
Common Distribution Function

Let Zn = n−½(X1 + X2 + … + Xn), where {Xn} is a sequence of independent and identically distributed random variables with EX1 = 0, and a common distribution function F and characteristic function ω. Suppose |ω|r is integrable for some integer r ≥ 1. For all n ≥ r, then Zn has a probability density function fn obtained by using the inversion formula.

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