Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-23T18:39:53.624Z Has data issue: false hasContentIssue false
  • English
  • Français

Augmented truncations of infinite stochastic matrices

Published online by Cambridge University Press:  14 July 2016

Diana Gibson  and
E. Seneta
Diana Gibson*
Affiliation:
University of Sydney
E. Seneta*
Affiliation:
University of Sydney
*
∗Postal address: Department of Mathematical Statistics, University of Sydney, NSW 2006, Australia.
∗Postal address: Department of Mathematical Statistics, University of Sydney, NSW 2006, Australia.
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the problem of approximating the stationary distribution of a positive-recurrent Markov chain with infinite transition matrix P, by stationary distributions computed from (n × n) stochastic matrices formed by augmenting the entries of the (n × n) northwest corner truncations of P, as n →∞.

Keywords

STATIONARY DISTRIBUTIONAUGMENTATIONLAST-EXIT PROBABILITIESUPPER-HESSENBERGLOWER-HESSENBERG
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 3 , September 1987 , pp. 600 - 608
Copyright
Copyright © Applied Probability Trust 1987 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Allen, B., Anderssen, R. S. and Seneta, E. (1977) Computation of stationary measures for infinite Markov chains. TIMS Studies in the Management Sciences , Vol. 7. Algorithmic Methods in Probability, ed. Neuts, M. F., North-Holland, Amsterdam, pp. 13–23.Google Scholar
Gibson, D. and Seneta, E. (1986) Augmented truncations of infinite stochastic matrices. Technical Report, Department of Mathematical Statistics, University of Sydney, NSW 2006, Australia.Google Scholar
Golub, G. H. and Seneta, E. (1974) Computation of the stationary distribution of an infinite stochastic matrix of special form. Bull. Austral. Math. Soc. 10, 255–261.CrossRefGoogle Scholar
Seneta, E. (1967) Finite approximations to infinite non-negative matrices. Proc. Camb. Phil. Soc. 63, 983–992; Part II: Refinements and applications 64 (1968), 465–470.CrossRefGoogle Scholar
Seneta, E. (1980) Computing the stationary distribution for infinite Markov chains. Linear Algebra Appl. 34, 259–267.Google Scholar
Seneta, E. (1981) Non-Negative Matrices and Markov Chains, 2nd edn, Springer-Verlag, New York.Google Scholar
Wolf, D. (1975) Approximation homogener Markoff-Ketten mit abzahlbarem Zustandraum durch solche mit endlichem Zustandraum. In Proceedings in Operations Research 5, Physica-Verlag, Wurzburg, pp. 137–146.Google Scholar
Wolf, D. (1980) Approximation of the invariant probability measure of an infinite stochastic matrix. Adv. Appl. Prob. 12, 710–726.Google Scholar