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Moments and Central Limit Theorems for Some Multivariate Poisson Functionals
- Part of
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- Journal:
- Advances in Applied Probability / Volume 46 / Issue 2 / June 2014
- Published online by Cambridge University Press:
- 22 February 2016, pp. 348-364
- Print publication:
- June 2014
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- Article
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This paper deals with Poisson processes on an arbitrary measurable space. Using a direct approach, we derive formulae for moments and cumulants of a vector of multiple Wiener-Itô integrals with respect to the compensated Poisson process. Also, we present a multivariate central limit theorem for a vector whose components admit a finite chaos expansion of the type of a Poisson U-statistic. The approach is based on recent results of Peccati et al. (2010), combining Malliavin calculus and Stein's method; it also yields Berry-Esseen-type bounds. As applications, we discuss moment formulae and central limit theorems for general geometric functionals of intersection processes associated with a stationary Poisson process of k-dimensional flats in
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