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Limits for the superposition of m-dimensional point processes

Published online by Cambridge University Press:  14 July 2016

Ward Whitt
Ward Whitt*
Affiliation:
Yale University
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Abstract

To obtain a limit with independent components in the superposition of m-dimensional point processes, a condition corresponding to asymptotic independence must be included. When this condition is relaxed, convergence to limits with dependent components is possible. In either case, convergence of finite distributions alone implies tightness and thus weak convergence in the function space D[0, ∞) × … × D[0, ∞).

Keywords

POINT PROCESSESPOISSON PROCESSSUPERPOSITION OF POINT PROCESSESSUPERPOSITION OF m-DIMENSIONAL POINT PROCESSESSUM OF POINT PROCESSESPOISSON APPROXIMATIONSRENEWAL PROCESSESWEAK CONVERGENCETIGHTNESSWEAK CONVERGENCE OF POINT PROCESSES
Type
Short Communications
Information
Journal of Applied Probability , Volume 9 , Issue 2 , June 1972 , pp. 462 - 465
Copyright
Copyright © Applied Probability Trust 1972 

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References

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