On the Perron-Frobenius row and column eigenspace of infinite dimensional stochastic matrices: Some examples
Abstract
This paper shows, via examples, that the dimension of the row eigenspace for an irreducible infinite dimensional stochastic matrix P corresponding to the Perron-Frobenius eigenvalue 1 can be zero, one, d, or infinite.Infinite dimensionality can arise even when the associated Markov chain is positive recurrent.This is to be contrasted with the finite dimensional setting in which the Perron-Frobenius row and column eigenspace for stochastic matrices is always one dimensional in the presence of irreducibility.
Fields of Study & Subjects
Matrix Theory and Algorithms
Mathematical Dynamics and Fractals
Probability and Statistical Research
Publication details
- Journal / source
- Communications in Optimization Theory
- Volume
- 2026
- Issue
- 1
- Publication date
- 1 January 2026
- Language
- EN