Some results in the probabilistic theory of asymptotic uniform distribution modulo 1

  • R. M. Loynes


Uniform Distribution Stochastic Process Probabilistic Theory Mathematical Biology Distribution Modulo 
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  1. 1.
    Billingsley,P.: Convergence of Probability Measures. New York: Wiley 1968.Google Scholar
  2. 2.
    Davenport,H., Erdös,P., LeVeque,W.: On Weyl's criterion for uniform distribution. Michigan Math. J. 10, 311–314 (1963).Google Scholar
  3. 3.
    Hlawka,E.: Ein metrischer Satz in der Theorie der C-Gleichverteilung. Monatsh. Math. 74, 108–118 (1970).Google Scholar
  4. 4.
    Holewijn,P.J.: On the uniform distribution of sequences of random variables. Z. Wahrscheinlichkeitsth. verw. Gebiete 14, 89–92 (1969).Google Scholar
  5. 5.
    Kuipers,L., van der Steen, P.: Metric theorems in the theory of asymptotic distribution modulo 1. Indagationes Math. 28, 300–310 (1966).Google Scholar
  6. 6.
    Loynes,R.M.: On certain applications of the spectral representation of stationary processes. Z. Wahrscheinlichkeitsth. verw. Gebiete 5, 180–186 (1966).Google Scholar
  7. 7.
    Robbins,H.: On the equidistribution of sums of independent random variables. Proc. Amer. Math. Soc. 4, 786–799 (1953).Google Scholar
  8. 8.
    Breiman,L.: Probability. Addison Wesley 1968.Google Scholar
  9. 9.
    Doob,J.L.: Stochastic Processes. New York: Wiley 1953.Google Scholar
  10. 10.
    Grenander,U.: Probabilities on Algebraic Structures. New York: Wiley 1963.Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • R. M. Loynes
    • 1
  1. 1.Department of Probability and StatisticsUniversity of SheffieldSheffieldEngland

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