English
Related papers

Related papers: Multivariate normal approximation using Stein's me…

200 papers

We extend the functional Breuer-Major theorem by Nourdin and Nualart (2020) to the space of rough paths. The proof of tightness combines the multiplication formula for iterated Malliavin divergences, due to Furlan and Gubinelli (2019), with…

Probability · Mathematics 2026-02-19 Henri Elad Altman , Tom Klose , Nicolas Perkowski

Motivated by the omnipresence of extreme value distributions in limit theorems involving extremes of random processes, we adapt Stein's method to include these laws as possible target distributions. We do so by using the generator approach…

Probability · Mathematics 2025-07-02 Bruno Costacèque , Laurent Decreusefond

We compute explicit upper bounds on the distance between the law of a multivariate Gaussian distribution and the joint law of wavelets/needlets coefficients based on a homogeneous spherical Poisson field. In particular, we develop some…

Probability · Mathematics 2015-04-27 Claudio Durastanti , Domenico Marinucci , Giovanni Peccati

The framework of Stein's method for Poisson process approximation is presented from the point of view of Palm theory, which is used to construct Stein identities and define local dependence. A general result (Theorem…

Probability · Mathematics 2016-09-07 Louis H. Y. Chen , Aihua Xia

This paper provides a general framework for Stein's density method for multivariate continuous distributions. The approach associates to any probability density function a canonical operator and Stein class, as well as an infinite…

Probability · Mathematics 2023-04-27 Guillaume Mijoule , Martin Raič , Gesine Reinert , Yvik Swan

Quantitative convergence in Wasserstein distance is often easier to establish than that in total variation distance. We show that such bounds allowing subgeometric rates yield central limit theorems (CLTs) for additive functionals of Markov…

Statistics Theory · Mathematics 2025-11-25 Rui Jin , Aixin Tan

The Mat\'ern covariance function is a popular choice for modeling dependence in spatial environmental data. Standard Mat\'ern covariance models are, however, often computationally infeasible for large data sets. In this work, recent results…

Computation · Statistics 2015-03-19 David Bolin , Finn Lindgren

We introduce the notion of {\em covariance measure structure} for square integrable stochastic processes. We define Wiener integral, we develop a suitable formalism for stochastic calculus of variations and we make Gaussian assumptions only…

Probability · Mathematics 2007-05-23 Ida Kruk , Francesco Russo , Ciprian Tudor

We obtain explicit $p$-Wasserstein distance error bounds between the distribution of the multi-parameter MLE and the multivariate normal distribution. Our general bounds are given for possibly high-dimensional, independent and identically…

Statistics Theory · Mathematics 2021-12-28 Andreas Anastasiou , Robert E. Gaunt

In \cite{n-p-noncentral}, Nourdin and Peccati established a neat characterization of Gamma approximation on a fixed Wiener chaos in terms of convergence of only the third and fourth cumulants. In this paper, we provide an optimal rate of…

Probability · Mathematics 2019-02-08 Ehsan Azmoodeh , Peter Eichelsbacher , Lukas Knichel

We establish various bounds on the solutions to a Stein equation for Poisson approximation in Wasserstein distance with non-linear transportation costs. The proofs are a refinement of those in [Barbour and Xia (2006)] using the results in…

Probability · Mathematics 2020-04-01 Zhong-Wei Liao , Yutao Ma , Aihua Xia

Using entropic inequalities from information theory, we provide new bounds on the total variation and 2-Wasserstein distances between a conditionally Gaussian law and a Gaussian law with invertible covariance matrix. We apply our results to…

Probability · Mathematics 2025-06-04 Lucia Celli , Giovanni Peccati

The purpose of this paper is to establish the convergence in law of the sequence of "midpoint" Riemann sums for a stochastic process of the form f'(W), where W is a Gaussian process whose covariance function satisfies some technical…

Probability · Mathematics 2013-07-26 Daniel Harnett , David Nualart

Modelling random dynamical systems in continuous time, diffusion processes are a powerful tool in many areas of science. Model parameters can be estimated from time-discretely observed processes using Markov chain Monte Carlo (MCMC) methods…

Computation · Statistics 2020-10-12 Susanne Pieschner , Christiane Fuchs

We study fluctuations of mean-field interacting particle systems around their McKean--Vlasov limit. Our main result provides a uniform-in-time quantitative central limit theorem for the fluctuation process, with convergence rate of order…

Probability · Mathematics 2026-05-06 Solesne Bourguin , Konstantinos Spiliopoulos

We provide a general steady-state diffusion approximation result which bounds the Wasserstein distance between the reversible measure $\mu$ of a diffusion process and the measure $\nu$ of an approximating Markov chain. Our result is…

Probability · Mathematics 2022-03-15 Thomas Bonis

We present an adaptation of Stein's method of normal approximation to the study of both discrete- and continuous-time dynamical systems. We obtain new correlation-decay conditions on dynamical systems for a multivariate central limit…

Probability · Mathematics 2017-01-12 Olli Hella , Juho Leppänen , Mikko Stenlund

In this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound. Our approach does not rely on existence and…

Analysis of PDEs · Mathematics 2014-09-16 Sara Daneri , Giuseppe Savare

We derive Gaussian approximation bounds for $k$-Potential Nearest Neighbor ($k$-PNN) based random forest predictions based on a set of training points given by a Poisson process under fairly mild regularity assumptions on the data…

Statistics Theory · Mathematics 2025-05-06 Zhaoyang Shi , Chinmoy Bhattacharjee , Krishnakumar Balasubramanian , Wolfgang Polonik

We show that the approaches to global regularity of the d-bar Neumann problem via the methods listed in the title are equivalent when the conditions involved are suitably modified. These modified conditions are also equivalent to one that…

Complex Variables · Mathematics 2007-05-23 Emil J. Straube , Marcel K. Sucheston