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Poisson bounds for moments of shot noise processes. (English) Zbl 0575.60051
Stochastic processes (v(t), \(t\in R)\) are considered having the form \(v(t)=\sum_{i}f(t-x_ i,\beta_ i)\), where \(\Phi =\{[x_ i,\beta_ i]\}\) is a random marked point process on R with real-valued marks \(\beta_ i;\quad f: R\times R\to R\) is a measurable response function. For second order moments of (v(t)), monotonicity properties are proved with respect to increasing variability of the mark distribution or of the underlying (non-marked) point process \(\{x_ i\}\), respectively. In particular, simple bounds are obtained if \(\{x_ i\}\) has a smaller or larger variability than a Poisson process with the same intensity.

MSC:
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60K25 Queueing theory (aspects of probability theory)
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
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