  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.
