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Some remarks on a counter process

Published online by Cambridge University Press:  14 July 2016

Lajos Takács
Lajos Takács*
Affiliation:
Case Western Reserve University, Cleveland, Ohio
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Abstract

In 1968 Lampard determined some limit distributions for a counter process in which the input and output are independent Poisson processes. In 1974 Phatarfod dealt with the generalizations of Lampard's formulas for the case when the input and output form a bivariate Poisson process; however, his reasoning is erroneous. The object of this paper is to determine the correct limit distributions for the generalized process.

Keywords

COUNTER PROCESS WITH FEEDBACKLIMIT DISTRIBUTIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 3 , September 1976 , pp. 623 - 627
Copyright
Copyright © Applied Probability Trust 1976 

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References

[1] Lampard, D.G. (1968) A stochastic process whose successive intervals between events form a first order Markov chain. I. J. Appl. Prob. 5, 648–668.Google Scholar
[2] Phatarfod, R.M. (1974) Note on the reversible counters system of Lampard. J. Appl. Prob. 11, 624–628.Google Scholar