Estimation of stationary probability of semi-Markov Chains

2021 ◽  
Author(s):  
Nikolaos Limnios ◽  
Bei Wu
Keyword(s):  
Markov Chains ◽  
Stationary Probability

scholarly journals Light-tailed asymptotics of stationary probability vectors of Markov chains of GI/G/1 type

2005 ◽  
Vol 37 (04) ◽  
pp. 1075-1093 ◽  
Author(s):  
Quan-Lin Li ◽  
Yiqiang Q. Zhao
Keyword(s):  
Asymptotic Behavior ◽  
Markov Chain ◽  
Markov Chains ◽  
Asymptotic Analysis ◽  
Positive Solution ◽  
Generating Function ◽  
Spectral Properties ◽  
Stationary Probability ◽  
Probability Vector ◽  
Stationary Probability Vector

In this paper, we consider the asymptotic behavior of stationary probability vectors of Markov chains of GI/G/1 type. The generating function of the stationary probability vector is explicitly expressed by theR-measure. This expression of the generating function is more convenient for the asymptotic analysis than those in the literature. TheRG-factorization of both the repeating row and the Wiener-Hopf equations for the boundary row are used to provide necessary spectral properties. The stationary probability vector of a Markov chain of GI/G/1 type is shown to be light tailed if the blocks of the repeating row and the blocks of the boundary row are light tailed. We derive two classes of explicit expression for the asymptotic behavior, the geometric tail, and the semigeometric tail, based on the repeating row, the boundary row, or the minimal positive solution of a crucial equation involved in the generating function, and discuss the singularity classes of the stationary probability vector.

Geometric bounds on iterative approximations for nearly completely decomposable Markov chains

1990 ◽  
Vol 27 (03) ◽  
pp. 521-529 ◽  
Author(s):  
Guy Louchard ◽  
Guy Latouche
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Perturbation Analysis ◽  
Stochastic Matrix ◽  
Stationary Probability ◽  
Probability Vector ◽  
Finite Markov Chain ◽  
Stationary Probability Vector

We consider a finite Markov chain with nearly-completely decomposable stochastic matrix. We determine bounds for the error, when the stationary probability vector is approximated via a perturbation analysis.

scholarly journals Light-tailed asymptotics of stationary probability vectors of Markov chains of GI/G/1 type

2005 ◽  
Vol 37 (4) ◽  
pp. 1075-1093 ◽  
Author(s):  
Quan-Lin Li ◽  
Yiqiang Q. Zhao
Keyword(s):  
Asymptotic Behavior ◽  
Markov Chain ◽  
Markov Chains ◽  
Asymptotic Analysis ◽  
Positive Solution ◽  
Generating Function ◽  
Spectral Properties ◽  
Stationary Probability ◽  
Probability Vector ◽  
Stationary Probability Vector

In this paper, we consider the asymptotic behavior of stationary probability vectors of Markov chains of GI/G/1 type. The generating function of the stationary probability vector is explicitly expressed by the R-measure. This expression of the generating function is more convenient for the asymptotic analysis than those in the literature. The RG-factorization of both the repeating row and the Wiener-Hopf equations for the boundary row are used to provide necessary spectral properties. The stationary probability vector of a Markov chain of GI/G/1 type is shown to be light tailed if the blocks of the repeating row and the blocks of the boundary row are light tailed. We derive two classes of explicit expression for the asymptotic behavior, the geometric tail, and the semigeometric tail, based on the repeating row, the boundary row, or the minimal positive solution of a crucial equation involved in the generating function, and discuss the singularity classes of the stationary probability vector.

Geometric bounds on iterative approximations for nearly completely decomposable Markov chains

1990 ◽  
Vol 27 (3) ◽  
pp. 521-529 ◽  
Author(s):  
Guy Louchard ◽  
Guy Latouche
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Perturbation Analysis ◽  
Stochastic Matrix ◽  
Stationary Probability ◽  
Probability Vector ◽  
Finite Markov Chain ◽  
Stationary Probability Vector

We consider a finite Markov chain with nearly-completely decomposable stochastic matrix. We determine bounds for the error, when the stationary probability vector is approximated via a perturbation analysis.

scholarly journals Some generalized juggling processes (extended abstract)

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Arvind Ayyer ◽  
Jérémie Bouttier ◽  
Svante Linusson ◽  
François Nunzi
Keyword(s):  
Markov Chains ◽  
Closed Form ◽  
Stationary Probability ◽  
Normalization Factor ◽  
Finite Models ◽  
International Audience ◽  
Product Formulas

International audience We consider generalizations of juggling Markov chains introduced by Ayyer, Bouttier, Corteel and Nunzi. We first study multispecies generalizations of all the finite models therein, namely the MJMC, the add-drop and the annihilation models. We then consider the case of several jugglers exchanging balls. In all cases, we give explicit product formulas for the stationary probability and closed-form expressions for the normalization factor if known. On s’intéresse à des généralisations des chaînes de Markov de jonglage introduites par Ayyer, Bouttier, Corteel et Nunzi. On étudie d’abord des généralisations multiespèces de tous les modèles finis, à savoir le MJMC et les modèles d’add-drop et d’annihilation. On considère ensuite le cas de plusieurs jongleurs échangeant des balles entre eux. Dans chacun des cas, on donne une formule explicite sous forme de produit pour l’état stationnaire, ainsi qu’une forme réduite pour le facteur de normalisation dans les cas où l’on en connaît une.

Markov models—Markov chains

2019 ◽  
Vol 16 (8) ◽  
pp. 663-664 ◽  
Author(s):  
Jasleen K. Grewal ◽  
Martin Krzywinski ◽  
Naomi Altman
Keyword(s):  
Markov Chains ◽  
Markov Models
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