On the Convergence Rate in the Invariance Principle

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1985 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:Theory of Probability & Its Applications, volume 29, pages 550-553 (issn: 0040-585X, eissn: 1095-7219,

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Authors: Borovkov, A. A.;

doi: 10.1137/1129068

On the Convergence Rate in the Invariance Principle

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Abstract

Let H be a real separable Hilbert space. An estimate of the convergence rate in the invariance principle for H-valued random variables is obtained. The sequence of coordinates of the random variables is supposed to be martingale-difference.

Keywords

martingale-difference, Functional limit theorems; invariance principles, Limit theorems for vector-valued random variables (infinite-dimensional case), convergence rate in the invariance principle

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