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 LicenseTopics
Theories of Stochastic_Matrices
- Stochastic_Matrix
- Stochastic_Vector_PMF
- Stochastic_Matrix_Markov_Models
- Eigenspace
- Stochastic_Matrix_Perron_Frobenius