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

Mikołaj J. Kasprzak

Stochastic Processes and their Applications, 2020, vol. 130, issue 8, 4927-4967

Abstract: 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.

Keywords: Stein’s method, Functional convergence, Brownian motion, Exceedances of the scans process, U-statistics (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:8:p:4927-4967

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DOI: 10.1016/j.spa.2020.02.006

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