Stable measures and Stein's method: rates in the Central Limit Theorem and diffusion approximation

Thomas Bonis (1)

1 GEOMETRICA - Geometric computing

We present a way to apply Stein's method in order to bound the Wasserstein distance between a, possibly discrete, measure and the Gaussian measure using what we call stable measures. We apply this construction to obtain convergence rates in terms of Wasserstein distance, for orders $p\geq2$, in the Central Limit Theorem in dimension $1$ under precise moment conditions. We also establish a similar result for the Wasserstein distance of order $2$ in the multidimensional setting. In a second time, we generalize our construction to more general target measures and we show how it can be applied to stationary distributions of Markov chains in the context of diffusion approximation.

Domaines: Probabilités [math.PR]; Analyse fonctionnelle [math.FA]

Thomas Bonis. Stable measures and Stein's method: rates in the Central Limit Theorem and diffusion approximation. 2015. ⟨hal-01167372v1⟩