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In this paper, we consider a target random variable $Y \sim \CVG$ distributed according to a centered Variance--Gamma distribution. For a generic random element $F=I_2(f)$ in the second Wiener chaos with $\E[F^2]= \E[Y^2]$ we establish a…

Probability · Mathematics 2021-07-01 Ehsan Azmoodeh , Peter Eichelsbacher , Christoph Thäle

We present a straightforward formulation of Stein's method for the semicircular distribution, specifically designed for the analysis of non-commutative random variables. Our approach employs a non-commutative version of Stein's heuristic,…

Probability · Mathematics 2024-12-03 Mario Díaz , Arturo Jaramillo

We use the delta method and Stein's method to derive, under regularity conditions, explicit upper bounds for the distributional distance between the distribution of the maximum likelihood estimator (MLE) of a $d$-dimensional parameter and…

Statistics Theory · Mathematics 2020-02-04 Andreas Anastasiou , Robert E. Gaunt

This paper uses the generator approach of Stein's method to analyze the gap between steady-state distributions of Markov chains and diffusion processes. Until now, the standard way to invoke Stein's method for this problem was to use the…

Probability · Mathematics 2022-02-15 Anton Braverman

This work introduces a new general approach for the numerical analysis of stable equilibria to second order mean field games systems in cases where the uniqueness of solutions may fail. For the sake of simplicity, we focus on a simple…

Analysis of PDEs · Mathematics 2024-10-30 Jules Berry , Olivier Ley , Francisco J Silva

We study sample average approximations (SAA) of chance constrained programs. SAA methods typically approximate the actual distribution in the chance constraint using an empirical distribution constructed from random samples assumed to be…

Optimization and Control · Mathematics 2022-05-13 Shuhao Yan , Francesca Parise , Eilyan Bitar

We build on the formalism developed in [arXiv:1906.08372v1] to propose new representations of solutions to Stein equations. We provide new uniform and non uniform bounds on these solutions (a.k.a.\ Stein factors). We use these…

Probability · Mathematics 2019-11-14 Marie Ernst , Yvik Swan

It is shown that the inert properties of a stationary random process can be expressed in terms of the ratio of its correlation interval to the doubled variance. When using a fixed value of the Planck constant h as a proportionality factor,…

General Physics · Physics 2022-10-10 Mikhail Batanov-Gaukhman

In this paper we consider the unconstrained minimization problem of a smooth function in ${\mathbb{R}}^n$ in a setting where only function evaluations are possible. We design a novel randomized derivative-free algorithm --- the stochastic…

Optimization and Control · Mathematics 2019-05-08 El Houcine Bergou , Eduard Gorbunov , Peter Richtárik

We develop a functional Stein-Malliavin method in a non-diffusive Poissonian setting, thus obtaining a) quantitative central limit theorems for approximation of arbitrary non-degenerate Gaussian random elements taking values in a separable…

Probability · Mathematics 2023-04-17 Solesne Bourguin , Simon Campese , Thanh Dang

In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…

Computation · Statistics 2012-09-04 Efthymios G. Tsionas

Let $p \in (0, \infty)$ be a constant and let $\{\xi_n\} \subset L^p(\Omega, {\mathcal F}, \P)$ be a sequence of random variables. For any integers $m, n \ge 0$, denote $S_{m, n} = \sum_{k=m}^{m + n} \xi_k$. It is proved that, if there…

Probability · Mathematics 2010-12-21 Erkan Nane , Yimin Xiao , Aklilu Zeleke

Using lattice approximations of Euclidean space, we develop a way to approximate stable processes that are represented by stochastic integrals over Euclidean space. Via a stable version of the Lindeberg-Feller Theorem we show that the…

Probability · Mathematics 2013-02-19 Clément Dombry , Paul Jung

The systematics of different approximations within the self-energy-functional theory (SFT) is discussed for fermionic lattice models with local interactions. In the context of the SFT, an approximation is essentially given by specifying a…

Strongly Correlated Electrons · Physics 2009-11-11 Michael Potthoff

We obtain a Stein characterisation of the distribution of the product of two correlated normal random variables with non-zero means, and more generally the distribution of the sum of independent copies of such random variables. Our Stein…

Probability · Mathematics 2024-09-11 Robert E. Gaunt , Siqi Li , Heather L. Sutcliffe

In the present paper we obtain a new correlation inequality and use it for the purpose of extending the theory of the Almost Sure Local Limit Theorem to the case of lattice random sequences in the domain of attraction of a stable law. In…

Probability · Mathematics 2014-01-14 Rita Giuliano , Zbigniew S. Szewczak

We consider the approximation of the stationary distribution of the finite inclusion process with the Poisson-Dirichlet distribution. Using Stein's method, we derive an explicit bound for the approximation error, which is of order 1/N in…

Probability · Mathematics 2025-12-18 Han L. Gan

We initiate the study of distortion in stable matching. Concretely, we aim to design algorithms that have limited access to the agents' cardinal preferences and compute stable matchings of high quality with respect to some aggregate…

Computer Science and Game Theory · Computer Science 2026-02-17 Aris Filos-Ratsikas , Georgios Kalantzis

This paper takes the so-called probabilistic approach to the Strong Renewal Theorem (SRT) for multivariate distributions in the domain of attraction of a stable law. A version of the SRT is obtained that allows any kind of…

Probability · Mathematics 2017-03-16 Zhiyi Chi

The functional characterization of a measure, an essential but delicate aspect of Stein's method, is shown to be accessible for stable probability distributions on convex cones. This notion encompasses the usual stable distributions…

Probability · Mathematics 2026-04-02 Costacèque , Decreusefond