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On the characterization of point processes with the order statistic property without the moment condition

Published online by Cambridge University Press:  14 July 2016

Prem S. Puri
Prem S. Puri*
Affiliation:
Purdue University
*
∗Postal address: Department of Statistics, Purdue University, Mathematical Sciences Building, West Lafayette, IN 47907, U.S.A.
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Abstract

The paper characterizes point processes with the order statistic property without the unnecessary condition of finiteness of the first moment of the process, a condition imposed by previous researchers. It shows that the class of these processes is composed only of mixed Poisson processes up to a time-scale transformation and of the mixed sample processes. It also introduces a multivariate analog of the order statistic property and characterizes completely the class of multivariate point processes with this property.

Keywords

POINT PROCESSESORDER STATISTIC PROPERTYMIXED POISSON PROCESSESMIXED SAMPLE PROCESSESMULTIVARIATE ORDER STATISTIC POINT PROCESSESMARKOV PROCESSES
Type
Research Paper
Information
Journal of Applied Probability , Volume 19 , Issue 1 , March 1982 , pp. 39 - 51
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

These investigations were supported in part by the U.S. National Science Foundation Grant No. MCS-7903704.

References

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