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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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