| Autor: |
LAST, GÜNTER, PENROSE, MATHEW D., SCHULTE, MATTHIAS, THÄLE, CHRISTOPH |
| Předmět: |
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| Zdroj: |
Advances in Applied Probability; Jun2014, Vol. 46 Issue 2, p348-364, 17p |
| Abstrakt: |
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 ℝd. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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