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For integer valued random variables, the translated Poisson distributions form a flexible family for approximation in total variation, in much the same way that the normal family is used for approximation in Kolmogorov distance. Using the…

Probability · Mathematics 2016-12-26 A. D. Barbour , Malwina J. Luczak , Aihua Xia

The variance-gamma (VG) distributions form a four parameter family that includes as special and limiting cases the normal, gamma and Laplace distributions. Some of the numerous applications include financial modelling and approximation on…

Probability · Mathematics 2020-02-18 Robert E. Gaunt

In this article, we present the theoretical basis for an approach to Stein's method for probability distributions on Riemannian manifolds. Using a semigroup representation for the solution to the Stein equation, we use tools from stochastic…

Probability · Mathematics 2020-01-28 James Thompson

In this paper we extend Stein's method to the distribution of the product of $n$ independent mean zero normal random variables. A Stein equation is obtained for this class of distributions, which reduces to the classical normal Stein…

Probability · Mathematics 2017-05-30 Robert E. Gaunt

In a recent paper, Gaunt 2020 extended Stein's method to limit distributions that can be represented as a function $g:\mathbb{R}^d\rightarrow\mathbb{R}$ of a centered multivariate normal random vector $\Sigma^{1/2}\mathbf{Z}$ with…

Probability · Mathematics 2022-09-21 Robert E. Gaunt , Heather Sutcliffe

In [Schuhmacher, Electron. J. Probab. 10 (2005), 165--201] estimates of the Barbour-Brown distance d_2 between the distribution of a thinned point process and the distribution of a Poisson process were derived by combining discretization…

Probability · Mathematics 2007-05-23 Dominic Schuhmacher

We propose a new minimum-distance estimator for linear random coefficient models. This estimator integrates the recently advanced sliced Wasserstein distance with the nearest neighbor methods, both of which enhance computational efficiency.…

Statistics Theory · Mathematics 2025-04-25 Keunwoo Lim , Ting Ye , Fang Han

We use Stein's method to bound the Wasserstein distance of order $2$ between a measure $\nu$ and the Gaussian measure using a stochastic process $(X_t)_{t \geq 0}$ such that $X_t$ is drawn from $\nu$ for any $t > 0$. If the stochastic…

Probability · Mathematics 2020-05-12 Thomas Bonis

Stein's method provides a way of bounding the distance of a probability distribution to a target distribution $\mu$. Here we develop Stein's method for the class of discrete Gibbs measures with a density $e^V$, where $V$ is the energy…

Probability · Mathematics 2008-08-22 Peter Eichelsbacher , Gesine Reinert

We discuss Stein's method for approximation by the stationary distribution of a single-birth Markov chain, in conjunction with stochastic monotonicity and similar assumptions. We use bounds on the increments of the solution of Poisson's…

Probability · Mathematics 2024-11-08 Fraser Daly

In this article we propose a general framework for normal approximation using Stein's method. We introduce the new concept of Stein couplings and we show that it lies at the heart of popular approaches such as the local approach,…

Probability · Mathematics 2010-10-27 Louis H. Y. Chen , Adrian Röllin

This paper studies the steady-state properties of the Join the Shortest Queue model in the Halfin-Whitt regime. We focus on the process tracking the number of idle servers, and the number of servers with non-empty buffers. Recently,…

Probability · Mathematics 2019-06-12 Anton Braverman

In this article, we discuss the basic ideas of a general procedure to adapt the Stein-Chen method to bound the distance between conditional distributions. From an integration-by-parts formula (IBPF), we derive a Stein operator whose…

Probability · Mathematics 2017-10-25 Alberto Chiarini , Alessandra Cipriani , Giovanni Conforti

Peccati, Sole, Taqqu, and Utzet recently combined Stein's method and Malliavin calculus to obtain a bound for the Wasserstein distance of a Poisson functional and a Gaussian random variable. Convergence in the Wasserstein distance always…

Probability · Mathematics 2014-09-09 Matthias Schulte

We propose a new functional analytic approach to Stein's method of exchangeable pairs that does not require the pair at hand to satisfy any approximate linear regression property. We make use of this theory in order to derive abstract…

Probability · Mathematics 2020-08-13 Christian Döbler

We derive a relation between the dissipation in a stochastic dynamics and the Wasserstein distance. We show that the minimal amount of dissipation required to transform an initial state to a final state during a diffusion process is given…

Statistical Mechanics · Physics 2019-12-19 Andreas Dechant , Yohei Sakurai

We adapt Stein's method of diffusion approximations, developed by Barbour, to the study of chaotic dynamical systems. We establish an error bound in the functional central limit theorem with respect to an integral probability metric of…

Dynamical Systems · Mathematics 2025-11-05 Juho Leppänen , Yuto Nakajima , Yushi Nakano

We provide new convergence guarantees in Wasserstein distance for diffusion-based generative models, covering both stochastic (DDPM-like) and deterministic (DDIM-like) sampling methods. We introduce a simple framework to analyze…

Machine Learning · Computer Science 2025-11-14 Eliot Beyler , Francis Bach

The paper is concerned with the equilibrium distributions of continuous-time density dependent Markov processes on the integers. These distributions are known typically to be approximately normal, and the approximation error, as measured in…

Probability · Mathematics 2009-02-06 Sanda N. Socoll , A. D. Barbour

We develop connections between Stein's approximation method, logarithmic Sobolev and transport inequalities by introducing a new class of functional inequalities involving the relative entropy, the Stein kernel, the relative Fisher…

Probability · Mathematics 2014-07-24 Michel Ledoux , Ivan Nourdin , Giovanni Peccati