On Borovkov's estimate in the Invariance Principle

Alexander Sakhanenko

doi:10.33048/semi.2019.16.125

On Borovkov's estimate in the Invariance Principle

Alexander Sakhanenko

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

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Аннотация

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.

Язык оригинала	английский
Страницы (с-по)	1776-1784
Число страниц	9
Журнал	Сибирские электронные математические известия
Том	16
DOI	https://doi.org/10.33048/semi.2019.16.125
Состояние	Опубликовано - 2019

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10.33048/semi.2019.16.125

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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",

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

В: Сибирские электронные математические известия, Том 16, 2019, стр. 1776-1784.

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

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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

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DO - 10.33048/semi.2019.16.125

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JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -

On Borovkov's estimate in the Invariance Principle

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