A note on simultaneous recurrence conditions on a set of denumerable stochastic matrices

1978 ◽  
Vol 15 (4) ◽  
pp. 842-847 ◽  
Author(s):  
A. Federgruen ◽  
A. Hordijk ◽  
H. C. Tijms
Keyword(s):  
Markov Chain ◽  
Stochastic Control ◽  
Metric Space ◽  
Considerable Extent ◽  
Control Problems ◽  
Stochastic Matrices ◽  
Compact Metric Space ◽  
Stochastic Control Problems ◽  
Markov Chain Theory ◽  
Chain Theory

In this paper we consider a set of denumerable stochastic matrices where the parameter set is a compact metric space. We give a number of simultaneous recurrence conditions on the stochastic matrices and establish equivalences between these conditions. The results obtained generalize corresponding results in Markov chain theory to a considerable extent and have applications in stochastic control problems.

A note on simultaneous recurrence conditions on a set of denumerable stochastic matrices

1978 ◽  
Vol 15 (04) ◽  
pp. 842-847 ◽  
Author(s):  
A. Federgruen ◽  
A. Hordijk ◽  
H. C. Tijms
Keyword(s):  
Markov Chain ◽  
Stochastic Control ◽  
Metric Space ◽  
Considerable Extent ◽  
Control Problems ◽  
Stochastic Matrices ◽  
Compact Metric Space ◽  
Stochastic Control Problems ◽  
Markov Chain Theory ◽  
Chain Theory

In this paper we consider a set of denumerable stochastic matrices where the parameter set is a compact metric space. We give a number of simultaneous recurrence conditions on the stochastic matrices and establish equivalences between these conditions. The results obtained generalize corresponding results in Markov chain theory to a considerable extent and have applications in stochastic control problems.

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.

Finite non-homogeneous Markov chains: Asymptotic behaviour

1976 ◽  
Vol 8 (3) ◽  
pp. 502-516 ◽  
Author(s):  
Harry Cohn
Keyword(s):  
Markov Chain ◽  
Asymptotic Behaviour ◽  
Transition Probabilities ◽  
Homogeneous Markov Chain ◽  
Stochastic Matrices ◽  
Weak Ergodicity ◽  
General Picture ◽  
Markov Chain Theory ◽  
Chain Theory ◽  
Probabilistic Nature

The paper is concerned with aspects of the behaviour of the products of finite stochastic matrices, the methods used in the proofs being of a probabilistic nature. The main result of the paper (Theorem 1) presents a general picture of the asymptotic behaviour of the transition probabilities between various groups of states. A unified treatment of some results of non-homogeneous Markov chain theory pertaining to weak ergodicity is then given.

Finite non-homogeneous Markov chains: Asymptotic behaviour

1976 ◽  
Vol 8 (03) ◽  
pp. 502-516 ◽  
Author(s):  
Harry Cohn
Keyword(s):  
Markov Chain ◽  
Asymptotic Behaviour ◽  
Transition Probabilities ◽  
Homogeneous Markov Chain ◽  
Stochastic Matrices ◽  
Weak Ergodicity ◽  
General Picture ◽  
Markov Chain Theory ◽  
Chain Theory ◽  
Probabilistic Nature

The paper is concerned with aspects of the behaviour of the products of finite stochastic matrices, the methods used in the proofs being of a probabilistic nature. The main result of the paper (Theorem 1) presents a general picture of the asymptotic behaviour of the transition probabilities between various groups of states. A unified treatment of some results of non-homogeneous Markov chain theory pertaining to weak ergodicity is then given.

Towards consensus: some convergence theorems on repeated averaging

1977 ◽  
Vol 14 (1) ◽  
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.

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