This article is cited in 35 papers

Estimates in the invariance principle in terms of truncated power moments

A. I. Sakhanenko

Ugra State University

Abstract: We obtain estimates for the distributions of errors which arise in approximation of a random polygonal line by a Wiener process on the same probability space. The polygonal line is constructed on the whole axis for sums of independent nonidentically distributed random variables and the distance between it and the Wiener process is taken to be the uniform distance with an increasing weight. All estimates depend explicitly on truncated power moments of the random variables which is an advantage over the earlier estimates of Komlos, Major, and Tusnady where this dependence was implicit.

Keywords: invariance principle, Prokhorov distance, method of the same probability space, rate of convergence, unimprovable estimates.

UDC: 519.214

Received: 30.05.2006

 English version: Siberian Mathematical Journal, 2006, 47:6, 1113–1127

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