scholarly journals Robust state observer of continues-time inhomogeneous Markov chain

2021 ◽  
pp. 74-79
Author(s):  
Evgenii A. Perepelkin ◽  
Keyword(s):  
Markov Chain ◽  
State Observer ◽  
Inhomogeneous 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.

Towards consensus: some convergence theorems on repeated averaging

1977 ◽  
Vol 14 (01) ◽  
pp. 89-97 ◽  
Author(s):  
S. Chatterjee ◽  
E. Seneta
Keyword(s):  
Markov Chain ◽  
Consensus Problem ◽  
Stochastic Matrices ◽  
Convergence Theorems ◽  
Strong Ergodicity ◽  
Markov Chain Theory ◽  
Inhomogeneous Markov Chain ◽  
Chain Theory ◽  
Equivalent Conditions

The problem of tendency to consensus in an information-exchanging operation is connected with the ergodicity problem for backwards products of stochastic matrices. For such products, weak and strong ergodicity, defined analogously to these concepts for forward products of inhomogeneous Markov chain theory, are shown (in contrast to that theory) to be equivalent. Conditions for ergodicity are derived and their relation to the consensus problem is considered.

scholarly journals An Entropy Rate Theorem for a Hidden Inhomogeneous Markov Chain

2017 ◽  
Vol 8 (1) ◽  
pp. 19-26
Author(s):  
Yao Qi-feng ◽  
Dong Yun ◽  
Wang Zhong-Zhi
Keyword(s):  
Stochastic Process ◽  
Markov Chain ◽  
Hidden Markov ◽  
The Other ◽  
Entropy Rate ◽  
Hidden Markov Chain ◽  
Mild Conditions ◽  
Ergodic Properties ◽  
Inhomogeneous Markov Chain ◽  
Flexible Application

Objective: The main object of our study is to extend some entropy rate theorems to a Hidden Inhomogeneous Markov Chain (HIMC) and establish an entropy rate theorem under some mild conditions. Introduction: A hidden inhomogeneous Markov chain contains two different stochastic processes; one is an inhomogeneous Markov chain whose states are hidden and the other is a stochastic process whose states are observable. Materials and Methods: The proof of theorem requires some ergodic properties of an inhomogeneous Markov chain, and the flexible application of the properties of norm and the bounded conditions of series are also indispensable. Results: This paper presents an entropy rate theorem for an HIMC under some mild conditions and two corollaries for a hidden Markov chain and an inhomogeneous Markov chain. Conclusion: Under some mild conditions, the entropy rates of an inhomogeneous Markov chains, a hidden Markov chain and an HIMC are similar and easy to calculate.

Convergence and finite-time behavior of simulated annealing

1986 ◽  
Vol 18 (03) ◽  
pp. 747-771 ◽  
Author(s):  
Debasis Mitra ◽  
Fabio Romeo ◽  
Alberto Sangiovanni-Vincentelli
Keyword(s):  
Markov Chain ◽  
Simulated Annealing ◽  
Finite Time ◽  
Randomized Algorithm ◽  
Global Optimum ◽  
Time Behavior ◽  
Annealing Schedule ◽  
Complete Problems ◽  
Inhomogeneous Markov Chain ◽  
Np Complete

Simulated annealing is a randomized algorithm which has been proposed for finding globally optimum least-cost configurations in large NP-complete problems with cost functions which may have many local minima. A theoretical analysis of simulated annealing based on its precise model, a time-inhomogeneous Markov chain, is presented. An annealing schedule is given for which the Markov chain is strongly ergodic and the algorithm converges to a global optimum. The finite-time behavior of simulated annealing is also analyzed and a bound obtained on the departure of the probability distribution of the state at finite time from the optimum. This bound gives an estimate of the rate of convergence and insights into the conditions on the annealing schedule which gives optimum performance.

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