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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 |
| Status: [ok] | This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations. |
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