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 normalized 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.
"A Markov chain representation of the normalized Perron–Frobenius eigenvector." Electron. Commun. Probab. 22 1 - 6, 2017. https://doi.org/10.1214/17-ECP76