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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2019, Volume 16, Pages 1776–1784
DOI: https://doi.org/10.33048/semi.2019.16.125 (Mi semr1166) 		 
This article is cited in 3 scientific papers (total 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
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DOI: https://doi.org/10.33048/semi.2019.16.125
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.
Funding agency Grant number
Russian Science Foundation 17-11-01173
This work is supported by the Russian Science Foundation under grant No. 17-11-01173.
Received October 27, 2019, published November 29, 2019
Bibliographic databases:
Document Type: Article
UDC: 519.214
MSC: 60F17
Language: English
Citation: A. I. Sakhanenko, “On Borovkov's estimate in the Invariance Principle”, Sib. Èlektron. Mat. Izv., 16 (2019), 1776–1784
Citation in format AMSBIB
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\by A.~I.~Sakhanenko
\paper On Borovkov's estimate in the Invariance Principle
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 1776--1784
\mathnet{http://mi.mathnet.ru/semr1166}
\crossref{https://doi.org/10.33048/semi.2019.16.125}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000501163400005}
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