  Let $A$ be a primitive matrix and let $\lambda$ 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.
