scholarly journals A local limit theorem for random walk defined on a finite Markov chain with absorbing barriers

2002 ◽  
Vol 25 (3) ◽  
pp. 301-308
Author(s):  
Toshiyuki Takenami ◽  
Michio Shimura
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Limit Theorem ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Finite Markov Chain

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  

A local limit theorem for random walk maxima with heavy tails

2002 ◽  
Vol 56 (4) ◽  
pp. 399-404 ◽  
Author(s):  
Søren Asmussen ◽  
Vladimir Kalashnikov ◽  
Dimitrios Konstantinides ◽  
Claudia Klüppelberg ◽  
Gurami Tsitsiashvili
Keyword(s):  
Random Walk ◽  
Limit Theorem ◽  
Heavy Tails ◽  
Local Limit Theorem ◽  
Local Limit

scholarly journals DYNAMIC QUANTUM BERNOULLI RANDOM WALKS

2008 ◽  
Vol 11 (02) ◽  
pp. 213-229
Author(s):  
NADINE GUILLOTIN-PLANTARD ◽  
RENÉ SCHOTT
Keyword(s):  
Random Walk ◽  
Limit Theorem ◽  
Random Walks ◽  
Limit Theorems ◽  
Law Of Large Numbers ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Large Numbers

Quantum Bernoulli random walks can be realized as random walks on the dual of SU(2). We use this realization in order to study a model of dynamic quantum Bernoulli random walk with time-dependent transitions. For the corresponding dynamic random walk on the dual of SU(2), we prove several limit theorems (local limit theorem, central limit theorem, law of large numbers, large deviation principle). In addition, we characterize a large class of transient dynamic random walks.

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.

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

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