Moments and Central Limit Theorems for Some Multivariate Poisson Functionals

@article{Last2014MomentsAC,
  title={Moments and Central Limit Theorems for Some Multivariate Poisson Functionals},
  author={G. Last and M. Penrose and M. Schulte and C. Th{\"a}le},
  journal={Advances in Applied Probability},
  year={2014},
  volume={46},
  pages={348 - 364}
}
  • G. Last, M. Penrose, +1 author C. Thäle
  • Published 2014
  • Mathematics
  • Advances in Applied Probability
  • 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… CONTINUE READING
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