Pacific Journal of Mathematics

Ergodic properties of nonnegative matrices. II.

D. Vere-Jones

Article information

Source
Pacific J. Math., Volume 26, Number 3 (1968), 601-620.

Dates
First available in Project Euclid: 13 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102985747

Mathematical Reviews number (MathSciNet)
MR0236745

Zentralblatt MATH identifier
0351.60069

Subjects
Primary: 47.30
Secondary: 15.00

Citation

Vere-Jones, D. Ergodic properties of nonnegative matrices. II. Pacific J. Math. 26 (1968), no. 3, 601--620. https://projecteuclid.org/euclid.pjm/1102985747


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References

  • [1] F. F. Bonsall Lectures on some fixed point theorems of functionalanalysis, Tata Institute of Fundamental Research, Bombay, 1962.
  • [2] A. Brauer, A new proof of theorems of Perron and Frobenius on non-negative matrices.I, positive matrices, Duke Math. J. 24 (1957), 367-78.
  • [3] N. Dunford and J. Schwartz, Linear Operators, Part I, Interscience Publishers, New York, 1958.
  • [4] P. T. Holmes, On some spectral properties of a transition matrix,Sankhya (Ser. A) 28 (1966), 205-214.Corrigendum Ibid 29 (1967), 106.
  • [5] S. Karlin, Positive operators, J. Math, and Mech. 8 (1959), 907-37.
  • [6] D. G. Kendall, Unitary Dilations of Markov transition operators..., In U.Grenander (Ed.) " Probability and Statistics" (Cramer Memorial Volume) Stockholm (Almqvist and Wiksell), 1959.
  • [7] S. C. Moy, -continuous Markov chains-II, Trans. Am. Math. Soc. 120 (1965) 83-107.
  • [8] S. C. Moy, Ergodic properties of expectation matrices of a branching process with countably many types, J. Math, and Mech. 16 (1966), 1201-1225.
  • [9] E. J. Nelson, The adjoint Markov process, Duke Math. J. 25 (1958), 671-90.
  • [10] C. R. Putnam, A note on nonnegative matrices, Canad. J. Math. 13 (1961), 59-62.
  • [11] F. Riesz and B. Sz-Nagy, Uber Kontraktionendes Hilbertschen Raumes, Acta Sci. Math. Szeged. 10 (1943), 202-5.
  • [12] F. Riesz and B. Sz-Nagy, Legons d'Analyse Fonctionelle, Budapest, 1953.
  • [13] H. Schaeffer, On the singularities of an analytic function with values in a Banach space, Arch. Math. 11 (1960), 40-43.
  • [14] E. Seneta and D. Vere-Jones, On quasistationary distributions..., J. Applied Prob. 3 (1966), 403-34.
  • [15] Z. Sidak, Eigenvaluesof operators in lP spaces in denumerableMarkov chains, Czech. Math. J. 14 (1964), 438-443.
  • [16] Z. Sidak, Some theorems and examples in the theory of operators indenumerable Markov chains, (in Czech), Casopis pro pestovan matematiky 88 (1963), 457-478.
  • [17] D. Vere-Jones, Topics in the Theory of Probability, (D. Phil. Thesis, Oxford, 1961).
  • [18] D. Vere-Jones, Spectral properties of some operators associated with queueing systems, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete. 2 (1963), 12-21.
  • [19] D. Vere-Jones, Ergodic properties of nonnegative matrices-I, Pacific J. Math. (2) 22 (1967), 361-386.

See also

  • I : D. Vere-Jones. Ergodic properties of nonnegative matrices. I. Pacific Journal of Mathematics volume 22, issue 2, (1967), pp. 361-386.