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The asymptotic covariance of two counters

Published online by Cambridge University Press:  24 October 2008

J. F. C. Kingman
Affiliation:
Mathematical Institute, University of Oxford

Abstract

A conjecture of Cox and Isham about the asymptotic form of the covariance of counts in two counters, linked by a partially shared input, is established by means of Smith's theory of cumulative processes and a variant of Wald's identity.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1977

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References

REFERENCES

(1)Cox, D. R. and Isham, V.A bivariate point process connected with electronic counters. Proc. Roy. Soc. A (to appear.)Google Scholar
(2)Doob, J. L.Stochastic processes (Wiley, 1953).Google Scholar
(3)Kingman, J. F. C.An application of the theory of regenerative phenomena. Proc. Cambridge Philos. Soc. 68 (1970), 697701.CrossRefGoogle Scholar
(4)Smith, W. L.Regenerative stochastic processes. Proc. Roy. Soc. A. 232 (1955), 631.Google Scholar
(5)Smith, W. L.Renewal theory and its ramifications. J. Roy. Statist. Soc. B. 20 (1958), 243302.Google Scholar