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Moments of stochastic processes governed by Poisson random measures. (English) Zbl 0724.60051
Let N be a Poisson random measure on a measurable space (E,\({\mathcal E})\) with \(\sigma\)-finite mean measure \(\nu\), and let f: \(E\to {\mathbb{R}}\) be a nonnegative \({\mathcal E}\)-measurable function. An explicit formula for the n-th moment of the random variable Nf by using the moments \(\nu f,\nu f^ 2,...,\nu f^ n\) of f is given.
Reviewer: P.Weiß (Linz)

MSC:
60G57 Random measures
60J75 Jump processes (MSC2010)
60J99 Markov processes
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