Stein’s method and normal approximation of Poisson functionals

New Berry-Esseen bounds for non-linear functionals of Poisson random measures*

This paper deals with the quantitative normal approximation of non-linear functionals of Poisson random measures, where the quality is measured by the Kolmogorov distance. Combining Stein’s method with the Malliavin calculus of variations on the Poisson space, we derive a bound, which is strictly smaller than what is available in the literature. This is applied to sequences of multiple integral...

Gaussian approximation of functionals: Malliavin calculus and Stein’s method

Combining Malliavin calculus and Stein’s method has recently lead to a new framework for normal and for chi-square approximation, and for second-order Poincaré inequalities. Applications include functionals of Gaussian random fields as well as functionals of infinite Poisson and Rademacher sequences. Here we present the framework and an extension which leads to invariance principles for multili...

Normal Approximation for White Noise Functionals by Stein’s Method and Hida Calculus

Stein Meets Malliavin in Normal Approximation

Stein’s method is a method of probability approximation which hinges on the solution of a functional equation. For normal approximation, the functional equation is a first-order differential equation. Malliavin calculus is an infinite-dimensional differential calculus whose operators act on functionals of general Gaussian processes. Nourdin and Peccati (Probab. Theory Relat. Fields 145(1–2), 75...

On Stein’s method and perturbations

Stein’s (1972) method is a very general tool for assessing the quality of approximation of the distribution of a random element by another, often simpler, distribution. In applications of Stein’s method, one needs to establish a Stein identity for the approximating distribution, solve the Stein equation and estimate the behaviour of the solutions in terms of the metrics under study. For some St...