Galton–Watson and branching process representations of the normalized Perron–Frobenius eigenvector - Archive ouverte HAL Access content directly
Journal Articles ESAIM: Probability and Statistics Year : 2019

Galton–Watson and branching process representations of the normalized Perron–Frobenius eigenvector

Abstract

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.
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Dates and versions

hal-03844582 , version 1 (08-11-2022)

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Raphaël Cerf, Joseba Dalmau. Galton–Watson and branching process representations of the normalized Perron–Frobenius eigenvector. ESAIM: Probability and Statistics, 2019, 23, pp.797-802. ⟨10.1051/ps/2019007⟩. ⟨hal-03844582⟩
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