Eugene Seneta. Non-Negative Matrices and Markov Chains. Springer Series in Statistics. Springer-Verlag, 1981. Home/Search Document Not in Database Summary Related Articles Check |
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Ergodic Theorems for Stochastic Operators and Discrete Event .. - Baccelli, Mairesse (9 citations) (Correct)
....operator T (x) Px is also interesting from the point of view of applications. It appeared in [21] to model the problem of reaching agreement on subjective opinions. More generally, it has been studied as a special case of the general theory of products of non negative matrices, see for example [41], Chapter 4.6. For any markovian matrix P , we have T ( 1) P 1 = 1. Hence the vector 1 is a generalized xed point (Def. 2.8) of operator T . By application of the 29 Perron Frobenius Theorem, it is the only one. Hence, applying the ergodic results of this paper to a stochastic sequence ....
....results (the convergence of (P n : P 0 x) to ( 1) In fact much stronger results are known for such models. The necessary and suOEcient conditions of convergence of (P n : P 0 x) to ( 1) are known for a general sequence of matrices P n , without any stochastic assumptions, see [41], Th. 4.18. max, linear systems Such operators have the following form ; i 2 f1; kg; T (x) i = max (x j a ij ) 8.3) T (x) A Omega x : 8.4) Equation (8.3) can be interpreted as a matrix vector product in the (max, algebra. Equation (8.4) is simply a rewriting of ....
E. Seneta. Non-negative Matrices and Markov Chains. Springer series in statistics. Springer Verlag, Berlin, 1981.
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Eugene Seneta. Non-Negative Matrices and Markov Chains. Springer Series in Statistics. Springer-Verlag, 1981.
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Eugene Seneta. Non-Negative Matrices and Markov Chains. Springer Series in Statistics. Springer-Verlag, 1981.
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E. Seneta, Non Negative Matrices and Markov Chains, Springer Verlag, New York, 1981. Gives the algebraic point of view on Markov chains.
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E. Seneta, Non-Negative Matrices and Markov Chains, Springer-Verlag New York Inc., 1981.
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