Pacific Journal of Mathematics

Ergodic properties of nonnegative matrices. I.

D. Vere-Jones

Article information

Source
Pacific J. Math., Volume 22, Number 2 (1967), 361-386.

Dates
First available in Project Euclid: 13 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102992207

Mathematical Reviews number (MathSciNet)
MR0214145

Zentralblatt MATH identifier
0171.15503

Subjects
Primary: 60.65
Secondary: 15.00

Citation

Vere-Jones, D. Ergodic properties of nonnegative matrices. I. Pacific J. Math. 22 (1967), no. 2, 361--386. https://projecteuclid.org/euclid.pjm/1102992207


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References

  • [1] E. Albert, Markov chains and -invariant measures, J. Math. Analysis and Ap- plications 6 (1963), 404-18.
  • [2] G. Birkhoff and R. S. Varga, Reactor criticalty and nonnegative matrices, J. Soc. Ind. and Applied Math. 6 (1958), 354-77.
  • [3] K. L. Chung, Markov Chains with Stationary Transition Probabilities, Berlin, 1960.
  • [4] C. Derman, A solution to a set of fundamental equations in Markov chains, Proc. Amer. Math. Soc. 5 (1954), 332-4.
  • [5] W. E. Feller, Introduction to Probability Theory and Its Applications (2nd Edition), New York, 1957.
  • [6] T. E. Harris, Transient Markov chains with stationarymeasures, Proc. Amer. Math. Soc. 8, (1957), 937-42.
  • [7] D. G. Kendall and G. E. H. Reuter, The calculation of the ergodic projection for Markov chains and processes with a countable infinity of states, Acta Math. 97 (1957), 103-44.
  • [8] J. F. C. Kingman, The exponential decay of Markov transition probabilities, Proc. Lond. Math. Soc. (Series 3) 13 (1963), 337-58.
  • [9] E. J. Nelson, The adjoint Markov process, Duke Math. J. 25 (1958), 671-90.
  • [10] W. E. Pruitt, Eigenvalues of non-negative matrices, Ann. Math. Stat 35 (1964), 1797-800.
  • [11] E. Seneta and D. Vere-Jones, On quasistationarydistributions in discrete-time Markov chains with a denumerable infinity of states, J. Applied Prob. 3 (1966), 403-434.
  • [12] Z. Sidak, Eigenvaluesof operators in denumerable Markov chains, Trans. 3rd Prague Conf. on Inf. Theory, Stat., Decision Functions, Random Processes 1962, Prague, (1963).
  • [13] Z. Sidak, Some theorems and examples in the theory of operators in denumerable Markov chains (in Czech), Casopis pro pestovan matematiky SS (1963), 457-78.
  • [14] Z. Sidak, Eigenvalues of operators in lP spaces in denumerable Markov chains, Czech. Math. J. (89) 14 (1964), 438-43.
  • [15] W. Veech, The necessity of Harris'condition for the existence of an invariant measure for transient Markov chains, Proc. Amer. Math. Soc. 14 (1963), 856-60.
  • [16] D. Vere-Jones, Topics in the Theory of Probability (D. Phil, thesis, Oxford), 1961.
  • [17] D. Vere-Jones, Geometric ergodicity in denumerable Markov chains, Quart. J. Math. (Oxford, 2) 13 (1962), 7-28.
  • [18] D. Vere-Jones, On the spectra of some linear operators associated with queueing systems, Z. Wahrscheinlichkeitstheorie 2 (1963), 12-21.
  • [19] D. Vere-Jones, A note on a theorem of Kingman and a theorem of Chung, Ann. Math. Statist. 37 (1966), 1844-1846.
  • [20] H. Wielandt, Unzerlegbare, nichtnegative Matrizen, Math. Z. 52 (1950), 642-8.

See also

  • II : D. Vere-Jones. Ergodic properties of nonnegative matrices. II. Pacific Journal of Mathematics volume 26, issue 3, (1968), pp. 601-620.