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Selective interaction of a Poisson and renewal process: the spectrum of the intervals between responses

Published online by Cambridge University Press:  14 July 2016

A. J. Lawrance
A. J. Lawrance*
Affiliation:
IBM Thomas J. Watson Research Center, Yorktown Heights, New York
*
* On leave of absence from the University of Leicester, England during the year 1970–71.
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Abstract

This paper is concerned with the spectrum of the intervals between responses in the renewal inhibited Poisson process, and continues the author's earlier work on this type of process ((1970a), (1970b), (1971)). A generating function for all the pairwise joint distributions of the synchronous intervals following an average response is obtained and leads directly to the associated serial correlations. It is shown that these correlations are equivalent to those predicted on different assumptions by the general stationary point theory. The results are then used to obtain the interval spectrum, and to exhibit a relationship between the sum of the serial correlations and the variance-time function. Explicit results for the spectrum of the renewal inhibited Poisson process are given for gamma inhibitory distributions, and the qualitative behavior is determined. Possible further developments are briefly discussed.

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 4 , December 1971 , pp. 731 - 744
Copyright
Copyright © Applied Probability Trust 1971 

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