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On Borovkov's estimate in the Invariance Principle. / Sakhanenko, Alexander.

In: Сибирские электронные математические известия, Vol. 16, 2019, p. 1776-1784.

Research output: Contribution to journal › Article › peer-review

Harvard

Sakhanenko, A 2019, 'On Borovkov's estimate in the Invariance Principle', Сибирские электронные математические известия, vol. 16, pp. 1776-1784. https://doi.org/10.33048/semi.2019.16.125

APA

Sakhanenko, A. (2019). On Borovkov's estimate in the Invariance Principle. Сибирские электронные математические известия, 16, 1776-1784. https://doi.org/10.33048/semi.2019.16.125

Vancouver

Sakhanenko A. On Borovkov's estimate in the Invariance Principle. Сибирские электронные математические известия. 2019;16:1776-1784. doi: 10.33048/semi.2019.16.125

Author

Sakhanenko, Alexander. / On Borovkov's estimate in the Invariance Principle. In: Сибирские электронные математические известия. 2019 ; Vol. 16. pp. 1776-1784.

BibTeX

@article{fe088d939b8c4da78daa65f5b4a9f7c7,
title = "On Borovkov's estimate in the Invariance Principle",
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{\textquoteright}s estimate. In addition, we have found similar but more precise estimates in terms of truncated Lyapunov fractions.",
keywords = "estimates in the Invariance Principle, Lyapunov fraction, Prokhorov distance, truncated Lyapunov fraction",
author = "Alexander Sakhanenko",
note = "Funding Information: Sakhanenko, A.I., On Borovkov{\textquoteright}s estimate in the Invariance Principle. ⃝c 2019 Sakhanenko A.I. This work is supported by the Russian Science Foundation under grant No. 17-11-01173.",
year = "2019",
doi = "10.33048/semi.2019.16.125",
language = "English",
volume = "16",
pages = "1776--1784",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",

}

RIS

TY - JOUR

T1 - On Borovkov's estimate in the Invariance Principle

AU - Sakhanenko, Alexander

N1 - Funding Information: Sakhanenko, A.I., On Borovkov’s estimate in the Invariance Principle. ⃝c 2019 Sakhanenko A.I. This work is supported by the Russian Science Foundation under grant No. 17-11-01173.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - estimates in the Invariance Principle

KW - Lyapunov fraction

KW - Prokhorov distance

KW - truncated Lyapunov fraction

UR - http://www.scopus.com/inward/record.url?scp=85097254104&partnerID=8YFLogxK

U2 - 10.33048/semi.2019.16.125

DO - 10.33048/semi.2019.16.125

M3 - Article

AN - SCOPUS:85097254104

VL - 16

SP - 1776

EP - 1784

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -

ID: 26207612