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Analyticity of Poisson-driven stochastic systems. (English) Zbl 0757.60045
Let \(\psi\) be a functional of the sample path of a stochastic system driven by a Poisson process with rate \(\lambda\). By using the well-known theorem of Bernstein that a function \(f: \mathbb{R}\to\mathbb{R}^ +\), which is absolutely monotonic in an interval \([a,b]\), is analytic there, it is shown in a very general setting that the expectation of \(\psi\), \(E_ \lambda(\psi)\), is an analytic function of \(\lambda\).
Reviewer: P.Weiß (Linz)

MSC:
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60K25 Queueing theory (aspects of probability theory)
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