D. Ferger, “Optimal bounds for the Prokhorov distance of the Miller–Sen process and Brownian motion”, Teor. Veroyatnost. i Primenen., 1997, Volume 42, Issue 1,Pages <nobr>202

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Optimal bounds for the Prokhorov distance of the Miller–Sen process and Brownian motion

D. Ferger

Mathematisches Institut, Justus-Liebig-Universität Giessen, Germany

Abstract: We consider U-processes introduced by Miller and Sen. Exact rates of convergence to Brownian motion in the sense of Prokhorov's metric are established.

Keywords: nondegenerate $U$-processes, the Prokhorov-metric, Hoeffding-decomposition, partial sum process.

Received: 23.03.1993

Language: English

DOI: 10.4213/tvp1723