Work

From asymptotic distribution and vague convergence to uniform convergence, with numerical applications

Year: 2025

Type: article

Abstract: Let { Λ n = { λ 1 , n , … , λ d n , n } } n ${\left\{{{\Lambda}}_{n}=\left\{{\lambda }_{1,n},\dots ,{\lambda }_{{d}_{n},n}\right\}\right\}}_{n}$ be a sequence of finite multisets of real numbers such that d n → ∞ as n → ∞, and let f : Ω ⊂ R d → R $f:{\Omega}\subset {\mathbb{R}}^{d}\to \mathbb{R}$ be a Lebesgue measurable function defined on a domain Ω with 0 < μ d (Ω) < ∞, where μ d is the Lebesgue measure in R d ${\mathbb{R}}^{d}$ . We say that { Λ n } n ${\left\{{{\Lambda}}_{n}\right\}}_{n}$ has an asymptotic distribution described by f , and we write { Λ n } n ∼ f ${\left\{{{\Lambda}}_{n}\right\}}_{n}\sim f$ , if (*)

Source: Journal of Numerical Mathematics

DOI: 10.1515/jnma-2023-0091

Authors: Giovanni Barbarino, Sven-Erik Ekström, Carlo Garoni, David Meadon, Stefano Serra-Capizzano, Paris Vassalos