Galton–Watson and branching process representations of the normalized Perron–Frobenius eigenvector
Résumé
Let A be a primitive matrix and let λ be its Perron–Frobenius eigenvalue. We give formulas expressing the associated normalized Perron–Frobenius eigenvector as a simple functional of a multitype Galton–Watson process whose mean matrix is A , as well as of a multitype branching process with mean matrix e ( A − I ) t . These formulas are generalizations of the classical formula for the invariant probability measure of a Markov chain.
Domaines
Mathématiques [math]| Origine | Fichiers produits par l'(les) auteur(s) |
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