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Truncation procedures for non-negative matrices

Published online by Cambridge University Press:  14 July 2016

Richard L. Tweedie
Richard L. Tweedie*
Affiliation:
University of Cambridge
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Extract

1. Let T = (tij), i, j = 0, 1, ···, tij ≧ 0, denote an infinite non-negative matrix. We shall assume at all times that where are the matrix iterates of T; we take T0 = I = (δij).

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 2 , June 1971 , pp. 311 - 320
Copyright
Copyright © Applied Probability Trust 1971 

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References

Chung, K. L. (1967) Markov Chains with Stationary Transition Probabilities. (2nd Ed.) Springer-Verlag, Berlin.Google Scholar
Jensen, A. and Kendall, D. G. (1971) Denumerable Markov processes with bounded generators: a routine for calculating pij(8). J. Appl. Prob. 8, 000–000.Google Scholar
Kendall, D. G. and Reuter, G. E. H. (1957) The calculation of the ergodic projection for Markov chains and processes with a countable infinity of states. Acta. Math. 97, 103–144.CrossRefGoogle Scholar
Kingman, J F. C. (1963) The exponential decay of Markov transition probabilities. Proc. Lond. Math. Soc. (3), 13, 337–358.Google Scholar
Seneta, E. (1967) Finite approximations to infinite non-negative matrices. Proc. Camb. Phil. Soc. 63, 983–992.Google Scholar
Seneta, E. (1968) Finite approximations to infinite non-negative matrices, II: refinements and applications. Proc. Camb. Phil. Soc. 64, 465–470.CrossRefGoogle Scholar
Vere-Jones, D. (1967) Ergodic properties of non-negative matrices, I. Pacific J. Math. 22, 361–386.CrossRefGoogle Scholar