Finite approximations to infinite non-negative matrices
- 24 October 1967
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 63 (4) , 983-992
- https://doi.org/10.1017/s0305004100042006
Abstract
In applying the theory of infinite Markov chains to practical examples, it is important to know how the ergodic properties defined by the infinite stochastic or substochastic matrix under consideration are related to those of the n × n (n = 1, 2, 3, …) truncated corner sub-matrices. In particular, it is of interest whether the relevant eigenvalues and eigenvectors of the truncated matrices in some sense approximate to corresponding quantities for the infinite matrix as n → ∞.Keywords
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