Asymptotic periodicity of the variances and covariances of the state sizes in non-homogeneous Markov systems

1988 ◽  
Vol 25 (1) ◽  
pp. 21-33 ◽  
Author(s):  
G. Tsaklidis ◽  
P.-C. G. Vassiliou
Keyword(s):  
Incidence Matrix ◽  
Stochastic Matrix ◽  
The State ◽  
Transition Matrices ◽  
Markov Systems ◽  
Stochastic Transition ◽  
Manpower System ◽  
Asymptotic Periodicity

In this paper we study the asymptotic periodicity of the sequence of means, variances and covariances of the state sizes of non-homogeneous Markov systems. It is proved that under the assumption that the sequence of the extended stochastic transition matrices converge to a matrix which is an irreducible stochastic matrix of period d, and all the matrices in this sequence have the same incidence matrix, then the sequence of means, variances and covariances splits into d subsequences which converge. Finally, we discuss the application of the present results in a manpower system.

Asymptotic periodicity of the variances and covariances of the state sizes in non-homogeneous Markov systems

1988 ◽  
Vol 25 (01) ◽  
pp. 21-33 ◽  
Author(s):  
G. Tsaklidis ◽  
P.-C. G. Vassiliou
Keyword(s):  
Incidence Matrix ◽  
Stochastic Matrix ◽  
The State ◽  
Transition Matrices ◽  
Markov Systems ◽  
Stochastic Transition ◽  
Manpower System ◽  
Asymptotic Periodicity

In this paper we study the asymptotic periodicity of the sequence of means, variances and covariances of the state sizes of non-homogeneous Markov systems. It is proved that under the assumption that the sequence of the extended stochastic transition matrices converge to a matrix which is an irreducible stochastic matrix of period d, and all the matrices in this sequence have the same incidence matrix, then the sequence of means, variances and covariances splits into d subsequences which converge. Finally, we discuss the application of the present results in a manpower system.

Non-homogeneous semi-Markov systems and maintainability of the state sizes

1992 ◽  
Vol 29 (3) ◽  
pp. 519-534 ◽  
Author(s):  
P.-C. G. Vassiliou ◽  
A. A. Papadopoulou
Keyword(s):  
Convex Set ◽  
Analytic Form ◽  
The State ◽  
Markov Systems ◽  
Markov System ◽  
Basic Parameters ◽  
Manpower System ◽  
Closed Analytic Form ◽  
First Time ◽  
Expected Duration

In this paper we introduce and define for the first time the concept of a non-homogeneous semi-Markov system (NHSMS). The problem of finding the expected population stucture is studied and a method is provided in order to find it in closed analytic form with the basic parameters of the system. Moreover, the problem of the expected duration structure in the state is studied. It is also proved that all maintainable expected duration structures by recruitment control belong to a convex set the vertices of which are specified. Finally an illustration is provided of the present results in a manpower system.

Non-homogeneous semi-Markov systems and maintainability of the state sizes

1992 ◽  
Vol 29 (03) ◽  
pp. 519-534 ◽  
Author(s):  
P.-C. G. Vassiliou ◽  
A. A. Papadopoulou
Keyword(s):  
Convex Set ◽  
Analytic Form ◽  
The State ◽  
Markov Systems ◽  
Markov System ◽  
Basic Parameters ◽  
Manpower System ◽  
Closed Analytic Form ◽  
First Time ◽  
Expected Duration

In this paper we introduce and define for the first time the concept of a non-homogeneous semi-Markov system (NHSMS). The problem of finding the expected population stucture is studied and a method is provided in order to find it in closed analytic form with the basic parameters of the system. Moreover, the problem of the expected duration structure in the state is studied. It is also proved that all maintainable expected duration structures by recruitment control belong to a convex set the vertices of which are specified. Finally an illustration is provided of the present results in a manpower system.

The size order of the state vector of discrete-time homogeneous Markov systems

2001 ◽  
Vol 38 (2) ◽  
pp. 357-368 ◽  
Author(s):  
I. Kipouridis ◽  
G. Tsaklidis
Keyword(s):  
Lower Bound ◽  
Discrete Time ◽  
State Vector ◽  
The State ◽  
Order Problem ◽  
Markov Systems ◽  
Markov System

The size order problem of the probability state vector elements of a homogeneous Markov system is examined. The time t0 is evaluated, after which the order of the state vector probabilities remains unchanged, and a formula to quickly find a lower bound for t0 is given. A formula for approximating the mode of the state sizes ni(t) as a function of the means Eni(t), and a relation to evaluate P(ni(t) = x+1) by means of certain terms which constitute P(ni(t) = x) are derived.

Positive columns for stochastic matrices

1974 ◽  
Vol 11 (4) ◽  
pp. 829-835 ◽  
Author(s):  
Dean Isaacson ◽  
Richard Madsen
Keyword(s):  
Positive Column ◽  
Stochastic Matrix ◽  
The State ◽  
Stochastic Matrices

If an n × n stochastic matrix has a column with no zeros, one can immediately conclude that the chain is ergodic and the state corresponding to that column is persistent and aperiodic. In this paper it is shown that it is decidable whether or not some power of a finite stochastic matrix has a positive column. Some problems regarding positive columns in infinite stochastic matrices are also considered.

scholarly journals Descriptor fractional linear systems with regular pencils

2013 ◽  
Vol 23 (2) ◽  
pp. 309-315 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Laplace Transform ◽  
Linear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
The State ◽  
Transition Matrices ◽  
State Equations ◽  
Numerical Examples ◽  
The Laplace Transform ◽  
Time Linear

Methods for finding solutions of the state equations of descriptor fractional discrete-time and continuous-time linear systems with regular pencils are proposed. The derivation of the solution formulas is based on the application of the Z transform, the Laplace transform and the convolution theorems. Procedures for computation of the transition matrices are proposed. The efficiency of the proposed methods is demonstrated on simple numerical examples.

Cheeger inequalities for absorbing Markov chains

2016 ◽  
Vol 48 (3) ◽  
pp. 631-647
Author(s):  
Gary Froyland ◽  
Robyn M. Stuart
Keyword(s):  
Markov Chains ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Transition Matrices ◽  
Stochastic Transition ◽  
Absorbing Markov Chains ◽  
Second Eigenvalue

Abstract We construct Cheeger-type bounds for the second eigenvalue of a substochastic transition probability matrix in terms of the Markov chain's conductance and metastability (and vice versa) with respect to its quasistationary distribution, extending classical results for stochastic transition matrices.

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