Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-25T04:41:02.393Z Has data issue: false hasContentIssue false
  • English
  • Français

Computation of the stationary distribution of an infinite Markov matrix

Published online by Cambridge University Press:  17 April 2009

G.H. Golub  and
E. Seneta
G.H. Golub
Affiliation:
Department of Computer Science, Stanford University, California, USA;
E. Seneta
Affiliation:
Department of Statistics, Princeton University, New Jersey, USA Department of Statistics, School of General Studies, Australian National University, Canberra, ACT.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

An algorithm is presented for computing the unique stationary distribution of an infinite stochastic matrix possessing at least one column whose elements are bounded away from zero. Elementwise convergence rate is discussed by means of two examples.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 8 , Issue 3 , June 1973 , pp. 333 - 341
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Бернштейн, С.Н. [Bernšteĭn, S.N.], Теория вероятностей, изд. 4-е [Probability theory, 4th edition] (Gostehizdat, Moscow, Leningrad, 1946).Google Scholar
[2]Feller, William, An introduction to probability theory and its applications. Volume 1, 3rd edition (John Wiley & Sons, New York, London, Sydney, 1968).Google Scholar
[3]Seneta, E., “Finite approximations to infinite non-negative matrices”, Proc. Cambridge Philos. Soc. 63 (1967), 983–992.CrossRefGoogle Scholar
[4]Seneta, E., “Finite approximations to infinite non-negative matrices, II: refinements and applications”, Proc. Cambridge Philos. Soc. 64 (1968), 465–470.CrossRefGoogle Scholar
[5]Styan, G.P.H., Personal communication (1970).Google Scholar