scholarly journals On the number of f-Recurrent runs and tuples in a finite markov chain

2019 ◽  
pp. 18-21
Author(s):  
N. M. Mezhennaya
Keyword(s):  
Markov Chain ◽  
Finite Markov Chain

STATE ESTIMATION OF A DISCRETE INHOMOGENEOUS MARKOV CHAIN

2021 ◽  
Author(s):  
E. A. Perepelkin ◽  
Keyword(s):  
Markov Chain ◽  
State Estimation ◽  
Finite Markov Chain ◽  
Luenberger Observer ◽  
Inhomogeneous Markov Chain

The problem of constructing a state estimation of inhomogeneous finite Markov chain based on a Luenberger observer is solved. The conditions of existence of the observer are defined. An algorithm for synthesizing the observer is described.

Perturbation bounds for the stationary probabilities of a finite Markov chain

1984 ◽  
Vol 16 (04) ◽  
pp. 804-818 ◽  
Author(s):  
Moshe Haviv ◽  
Ludo Van Der Heyden
Keyword(s):  
Markov Chain ◽  
Stationary Distribution ◽  
Finite Markov Chain ◽  
Perturbation Bounds ◽  
Aggregation Technique ◽  
Stationary Probabilities

This paper discusses perturbation bounds for the stationary distribution of a finite indecomposable Markov chain. Existing bounds are reviewed. New bounds are presented which more completely exploit the stochastic features of the perturbation and which also are easily computable. Examples illustrate the tightness of the bounds and their application to bounding the error in the Simon–Ando aggregation technique for approximating the stationary distribution of a nearly completely decomposable Markov chain.

Absorption Probabilities for Sums of Random Variables Defined on a Finite Markov Chain

1962 ◽  
Vol 58 (2) ◽  
pp. 286-298 ◽  
Author(s):  
H. D. Miller
Keyword(s):  
Markov Chain ◽  
Asymptotic Expression ◽  
Random Variables ◽  
Partial Sums ◽  
Finite Markov Chain ◽  
Initial State ◽  
Main Result Theorem ◽  
Sums Of Random Variables ◽  
Result Theorem ◽  
Image Position

SummaryThis paper is essentially a continuation of the previous one (5) and the notation established therein will be freely repeated. The sequence {ξr} of random variables is defined on a positively regular finite Markov chain {kr} as in (5) and the partial sums and are considered. Let ζn be the first positive ζr and let πjk(y), the ‘ruin’ function or absorption probability, be defined by The main result (Theorem 1) is an asymptotic expression for πjk(y) for large y in the case when , the expectation of ξ1 being computed under the unique stationary distribution for k0, the initial state of the chain, and unconditional on k1.

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