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On a characteristic property of point processes

Published online by Cambridge University Press:  09 April 2009

B. L. S. Prakasa Rao
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kanpur 208016, India.
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Abstract

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This note is concerned with a certain property of point processes. We prove that if N1, N2 and N3 are three independent point processes, then the bivariate point process (N1 + N3+ N2 + N3) uniquely determines the point processes N1, N2 and N3.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1976

References

Aczel, J. (1966), Lectures on functional equations and their applications (Academic Press, 1966).Google Scholar
Harris, T. E. (1963), The theory of branching processes (Springer-Verlag, 1963).CrossRefGoogle Scholar
Milne, R. K. (1970), ‘Identifiability for random translations of Poisson processes’, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 15, 195201.CrossRefGoogle Scholar
Vere-Jones, D. (1968), ‘Some applications of probability generating functionals to the study of input-output streams’, J. Roy. Statistic Soc. Ser. B 30, 321333.Google Scholar
Westcott, M. (1972), ‘The probability generating functional’, J. Austral. Math. Soc. 14, 448466.CrossRefGoogle Scholar