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On the moments of a self-correcting process

Published online by Cambridge University Press:  14 July 2016

D. Vere-Jones  and
Y. Ogata
D. Vere-Jones*
Affiliation:
Victoria University of Wellington
Y. Ogata*
Affiliation:
Institute of Statistical Mathematics, Tokyo
*
∗ Postal address: Department of Mathematics, Victoria University of Wellington, P.O. Box 196, Wellington, New Zealand.
∗∗ Postal address: The Institute of Statistical Mathematics, 4–6–7 Minami-Azabu, Minato-ku, Tokyo, Japan.
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Abstract

The existence of ordinary and exponential moments of a point process with conditional intensity of the form is deduced from a Markov chain representation for t – ρN(t). These results form an application of recent theorems of Tweedie (1983a, b) and are used to obtain laws of large numbers for a range of functionals of the process.

Keywords

SELF-CORRECTING POINT PROCESSMARKOV CHAINLAWS OF LARGE NUMBERSERGODIC BEHAVIOURWEIGHTED AVERAGES
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 2 , June 1984 , pp. 335 - 342
Copyright
Copyright © Applied Probability Trust 1984 

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References

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