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Graphes et algorithme de calcul de probabilités stationnaires d’un processus markovien discret. (Graphs and algorithm for the computation of stationary probabilities of a discrete Markov process). (French) Zbl 0701.60064
The author in effect addresses the problem of finding the (unique) stationary distribution \(\{p_ i\}^ n_{i=0}\) corresponding to a finite stochastic matrix \(P=\{p_{ij}\}^ n_{i,j=0}\) satisfying \(p_{ii}=0\) for each i, and containing only one closed set of indices. The approach depends on writing \[ p_ i=Z_ 1'R_ 1'...R'_{k- 1}S_{k,i}R_{k+1}...R_{n-1}Z_{n-1},\quad i\in E_ k,\quad k=0,...,n, \] as an inhomogeneous product of certain non-negative matrices, after decomposing the index set into mutually exclusive subsets \(\{E_ k\}\). The author is, consequently, able to use coefficients of ergodicity [see the reviewer, Non-negative matrices and Markov chains. (1981; Zbl 0471.60001)] as a measure of speed of convergence.

MSC:
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
Citations:
Zbl 0471.60001
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