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Moment formulae for general point processes. (English) Zbl 1297.60031
Summary: The goal of this paper is to generalize most of the moment formulae obtained in [N. Privault, Ann. Inst. Henri Poincaré, Probab. Stat. 48, No. 4, 947–972 (2012; Zbl 1278.60084)]. More precisely, we consider a general point process \(\mu\), and show that the quantities relevant to our problem are the so-called Papangelou intensities. When the Papangelou intensities of \(\mu\) are well-defined, we show some general formulae to recover the moment of order \(n\) of the stochastic integral of the point process. We will use these extended results to introduce a divergence operator and study a random transformation of the point process.

MSC:
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60H07 Stochastic calculus of variations and the Malliavin calculus
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