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 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  

On the local limit theorem for non-uniformly ergodic Markov chains

1995 ◽  
Vol 32 (1) ◽  
pp. 52-62 ◽  
Author(s):  
Marc Séva
Keyword(s):  
Markov Chain ◽  
Limit Theorem ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Exponential Moment ◽  
Countable State Space ◽  
Uniform Ergodicity ◽  
Countable State ◽  
Reflected Random Walk ◽  
Positive Half

Using an approach similar to that of Guivarc'h and Hardy (1988), we show that the local limit theorem holds for a Markov chain on a countable state space, with non-uniform ergodicity, when the recurrence is fast enough. We present a detailed study of a typical example, the reflected random walk on the positive half-line with negative mean and finite exponential moment. The results can be extended to some random walks on ℕ.

On the local limit theorem for non-uniformly ergodic Markov chains

1995 ◽  
Vol 32 (01) ◽  
pp. 52-62
Author(s):  
Marc Séva
Keyword(s):  
Markov Chain ◽  
Limit Theorem ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Exponential Moment ◽  
Countable State Space ◽  
Uniform Ergodicity ◽  
Countable State ◽  
Reflected Random Walk ◽  
Positive Half

Using an approach similar to that of Guivarc'h and Hardy (1988), we show that the local limit theorem holds for a Markov chain on a countable state space, with non-uniform ergodicity, when the recurrence is fast enough. We present a detailed study of a typical example, the reflected random walk on the positive half-line with negative mean and finite exponential moment. The results can be extended to some random walks on ℕ.

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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