A note on bounds and monotonicity of spatial stationary Cox shot noises
نویسنده
چکیده
We consider shot-noise processes and max-shot-noise processes driven by spatial stationary Cox (doubly stochastic Poisson) processes. We derive the upper and lower bounds of them 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 point process inputs lead to more variable shot-noises. These are direct applications of the results obtained for so-called Ross-type conjectures in queueing theory.
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