L\'evy systems and moment formulas for mixed Poisson integrals
Krzysztof Bogdan, Jan Rosi\'nski, Grzegorz Serafin, {\L}ukasz, Wojciechowski
TL;DR
This paper introduces Mecke-Palm formulas for mixed Poisson integrals and applies them to derive moment formulas for products of interlaced multiple Poisson integrals in Lévy processes.
Contribution
It presents new Mecke-Palm formulas for mixed Poisson integrals and derives novel moment formulas for Lévy process integrals.
Findings
Derived Mecke-Palm formulas for mixed Poisson integrals.
Obtained explicit moment formulas for products of Lévy process integrals.
Enhanced understanding of Lévy systems and their applications.
Abstract
We propose Mecke-Palm formulas for multiple integrals with respect to a Poisson random measure interlaced with its intensity measure. We apply such formulas to multiple mixed L\'evy systems of L\'evy processes and obtain moment formulas for products of interlaced multiple Poisson integrals.
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Taxonomy
TopicsRandom Matrices and Applications · Stochastic processes and financial applications · Geometry and complex manifolds