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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
##### Keywords:
Poisson random measure; moments
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