Stochastic Matrices and the Perron-Frobenius Theorem

 Title: Stochastic Matrices and the Perron-Frobenius Theorem Author: René Thiemann Submission date: 2017-11-22 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. BibTeX: @article{Stochastic_Matrices-AFP, author = {René Thiemann}, title = {Stochastic Matrices and the Perron-Frobenius Theorem}, journal = {Archive of Formal Proofs}, month = nov, year = 2017, note = {\url{http://isa-afp.org/entries/Stochastic_Matrices.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: Jordan_Normal_Form, Markov_Models, Perron_Frobenius