This article is cited in 18 papers

On the estimates of the rate of convergence in the invariance principle for Banach spaces

A. A. Borovkov, A. I. Sahanenko

Novosibirsk

Abstract: We propose a method for obtaining the estimates in the invariance principle for Banach spaces; this method doesn't use the representation on a common probability space. In particular, it is shown that the estimate proved by Borovkov [7] for the one- dimensional invariance principle remains valid for the finite-dimensional case too.

Received: 03.04.1980

 English version: Theory of Probability and its Applications, 1981, 25:4, 721–731

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