GENERALIZED CLASS [script C] MARKOV CHAINS AND COMPUTATION OF CLOSED-FORM BOUNDING DISTRIBUTIONS

2007 ◽  
Vol 21 (02) ◽  
Author(s):  
Mouad Ben Mamoun ◽  
Ana Bušic ◽  
Nihal Pekergin
Keyword(s):  
Markov Chains ◽  
Closed Form

scholarly journals On explicit form of the stationary distributions for a class of bounded Markov chains

2016 ◽  
Vol 53 (1) ◽  
pp. 231-243 ◽  
Author(s):  
S. McKinlay ◽  
K. Borovkov
Keyword(s):  
Markov Chains ◽  
Closed Form ◽  
State Space ◽  
Explicit Form ◽  
Discrete Time ◽  
Unit Interval ◽  
Time Step ◽  
Stationary Distributions ◽  
End Point ◽  
Current Location

AbstractWe consider a class of discrete-time Markov chains with state space [0, 1] and the following dynamics. At each time step, first the direction of the next transition is chosen at random with probability depending on the current location. Then the length of the jump is chosen independently as a random proportion of the distance to the respective end point of the unit interval, the distributions of the proportions being fixed for each of the two directions. Chains of that kind were the subjects of a number of studies and are of interest for some applications. Under simple broad conditions, we establish the ergodicity of such Markov chains and then derive closed-form expressions for the stationary densities of the chains when the proportions are beta distributed with the first parameter equal to 1. Examples demonstrating the range of stationary distributions for processes described by this model are given, and an application to a robot coverage algorithm is discussed.

CLOSED-FORM STOCHASTIC BOUNDS ON THE STATIONARY DISTRIBUTION OF MARKOV CHAINS

2002 ◽  
Vol 16 (4) ◽  
pp. 403-426 ◽  
Author(s):  
Mouad Ben Mamoun ◽  
Nihal Pekergin
Keyword(s):  
Markov Chains ◽  
Closed Form ◽  
Stationary Distribution ◽  
Discrete Time ◽  
Transition Probability ◽  
Matrix Structure ◽  
Stochastic Monotonicity ◽  
Monotonicity Properties ◽  
Transition Probability Matrices ◽  
Probability Matrices

We propose a particular class of transition probability matrices for discrete-time Markov chains with a closed form to compute the stationary distribution. The stochastic monotonicity properties of this class are established. We give algorithms to construct monotone, bounding matrices belonging to the proposed class for the variability orders. The accuracy of bounds with respect to the underlying matrix structure is discussed through an example.

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.

scholarly journals Different Closed-Form Expressions for Generalized Entropy Rates of Markov Chains

2018 ◽  
Vol 21 (4) ◽  
pp. 1431-1452
Author(s):  
Valérie Girardin ◽  
Loick Lhote ◽  
Philippe Regnault
Keyword(s):  
Markov Chains ◽  
Closed Form ◽  
Generalized Entropy
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