Stein's method and normal approximation of Poisson functionals

Details Stein's method and normal approximation of Poisson functionals Stein's method and normal approximation of Poisson functionals

2008-07-31

arxiv.org/abs/0807.5035v1

Mathematics

Probability

32 pages

Scientific paper

We combine Stein's method with a version of Malliavin calculus on the Poisson
space. As a result, we obtain explicit Berry-Ess\'een bounds in Central Limit
Theorems (CLTs) involving multiple Wiener-It\^o integrals with respect to a
general Poisson measure. We provide several applications to CLTs related to
Ornstein-Uhlenbeck L\'evy processes.

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