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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.

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.)
Full Text: DOI
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