This article is cited in 3 papers

Probability theory and mathematical statistics

On Borovkov's estimate in the Invariance Principle

A. I. Sakhanenko

Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia

Abstract: The first general estimate in the functional CLT (i.e. in the Invariance Principle) was obtained by A. Borovkov in 1973 in terms of the Lyapunov fractions of order not greater than three. Here we present explicit numerical bounds for the constants in Borovkov's estimate. In addition, we have found similar but more precise estimates in terms of truncated Lyapunov fractions.

Keywords: estimates in the Invariance Principle, Prokhorov distance, Lyapunov fraction, truncated Lyapunov fraction.

UDC: 519.214

MSC: 60F17

Received October 27, 2019, published November 29, 2019

Language: English

DOI: 10.33048/semi.2019.16.125

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