Articlebronze2010

Stein’s method and Normal approximation of Poisson functionals

Giovanni Peccati · Josep Lluís Solé · Murad S. Taqqu · Frederic Utzet

152 citations0/0 files storedThe Annals of Probability

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Stochastic processes and financial applications Probability and Statistical Research Point processes and geometric inequalities

Abstract

We combine Stein’s method with a version of Malliavin calculus on the Poisson space. As a result, we obtain explicit Berry–Esséen bounds in Central limit theorems (CLTs) involving multiple Wiener–Itô integrals with respect to a general Poisson measure. We provide several applications to CLTs related to Ornstein–Uhlenbeck Lévy processes.

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References

2001Non-Gaussian Ornstein–Uhlenbeck-based Models and Some of Their Uses in Financial Economics 2005Central limit theorems for sequences of multiple stochastic integrals 2008Stein’s method on Wiener chaos 2004Gaussian Limits for Vector-valued Multiple Stochastic Integrals 2007Central limit theorems for multiple stochastic integrals and Malliavin calculus

Cited by

2010Multi-Dimensional Gaussian Fluctuations on the Poisson Space 2010Stein's Method Meets Malliavin Calculus: A Short Survey With New Estimates 2013Lectures on Gaussian Approximations with Malliavin Calculus 2018The fourth moment theorem on the Poisson space

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