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The rate and variance functions arising from the interaction of two stationary point processes

Published online by Cambridge University Press:  14 July 2016

A. J. Lawrance
A. J. Lawrance*
Affiliation:
University of Birmingham
*
∗Postal address: Department of Mathematical Statistics, University of Birmingham, P.O. Box 363, Birmingham B15 2TT, U.K.
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Abstract

The paper gives the mean-time and variance-time functions of responses arising from a general type of interaction between two stationary point processes which are independent of each other. The mean-time function is obtained exactly and explicitly, thereby much improving on earlier work. A Laplace-transformed version of the variance-time function is derived under the general assumptions, and new results for the asymptotic slope and intercept are obtained when one of the point processes is renewal. Attention is drawn to the difficulties of dealing with non-renewal and non-regenerative point processes.

Keywords

STATIONARY POINT PROCESSINTERACTION OF POINT PROCESSESRENEWAL THEORYVARIANCE-TIME FUNCTIONNEURON FIRING MODEL
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 2 , June 1979 , pp. 287 - 296
Copyright
Copyright © Applied Probability Trust 1979 

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References

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