A Markov chain representation of the normalized Perron–Frobenius eigenvector
Résumé
We consider the problem of finding the Perron-Frobenius eigenvector of a primitive matrix. Dividing each of the rows of the matrix by the sum of the elements in the row, the resulting new matrix is stochastic. We give a formula for the Perron-Frobenius eigenvector of the original matrix, in terms of a realization of the Markov chain defined by the associated stochastic matrix. This formula is a generalization of the classical formula for the invariant probability measure of a Markov chain.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)