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A NOTE ON BOUNDS AND MONOTONICITY OF SPATIAL STATIONARY COX SHOT NOISES

Published online by Cambridge University Press:  01 October 2004

Naoto Miyoshi
Naoto Miyoshi
Affiliation:
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552, Japan, E-mail: [email protected]
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Abstract

We consider shot-noise and max-shot-noise processes driven by spatial stationary Cox (doubly stochastic Poisson) processes. We derive their upper and lower bounds in terms of the increasing convex order, which is known as the order relation to compare the variability of random variables. Furthermore, under some regularity assumption of the random intensity fields of Cox processes, we show the monotonicity result which implies that more variable shot patterns lead to more variable shot noises. These are direct applications of the results obtained for so-called Ross-type conjectures in queuing theory.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 18 , Issue 4 , October 2004 , pp. 561 - 571
Copyright
© 2004 Cambridge University Press

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References

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