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Finite approximations to infinite non-negative matrices

Published online by Cambridge University Press:  24 October 2008

E. Seneta
E. Seneta
Affiliation:
Australian National University
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Extract

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 → ∞.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 4 , October 1967 , pp. 983 - 992
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

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