Stein's method for multivariate Brownian approximations of sums under dependence

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Kasprzak, Mikolaj J.¹ 

[1] Univ Luxembourg, Dept Math, 6 Ave Fonte, L-4364 Luxembourg, Luxembourg

关键词: Stein's method;    Functional convergence;    Brownian motion;    Exceedances of the scans process;    U-statistics;   

DOI  :  10.1016/j.spa.2020.02.006

来源: Elsevier

【 摘 要 】

We use Stein's method to obtain a bound on the distance between scaled p-dimensional random walks and a p-dimensional (correlated) Brownian motion. We consider dependence schemes including those in which the summands in scaled sums are weakly dependent and their p components are strongly correlated. As an example application, we prove a functional limit theorem for exceedances in an m-scans process, together with a bound on the rate of convergence. We also find a bound on the rate of convergence of scaled U-statistics to Brownian motion, representing an example of a sum of strongly dependent terms. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free