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.
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