Stochastic Matrices and the Perron-Frobenius Theorem

René Thiemann 🌐

November 22, 2017

Abstract

Stochastic matrices are a convenient way to model discrete-time and finite state Markov chains. The Perron–Frobenius theorem tells us something about the existence and uniqueness of non-negative eigenvectors of a stochastic matrix. In this entry, we formalize stochastic matrices, link the formalization to the existing AFP-entry on Markov chains, and apply the Perron–Frobenius theorem to prove that stationary distributions always exist, and they are unique if the stochastic matrix is irreducible.
BSD License

Topics

Theories of Stochastic_Matrices