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Article Dans Une Revue Electronic Communications in Probability Année : 2017

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.
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Dates et versions

hal-03844575 , version 1 (08-11-2022)

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Raphaël Cerf, Joseba Dalmau. A Markov chain representation of the normalized Perron–Frobenius eigenvector. Electronic Communications in Probability, 2017, 22 (none), ⟨10.1214/17-ECP76⟩. ⟨hal-03844575⟩
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