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Sibirskii Matematicheskii Zhurnal, 2011, Volume 52, Number 4, Pages 876–893 (Mi smj2245)  

This article is cited in 5 scientific papers (total in 5 papers)

A general estimate in the invariance principle

A. I. Sakhanenko

Yugra State University, Khanty-Mansiĭsk, Russia
Full-text PDF (342 kB) Citations (5)
References:
Abstract: We obtain estimates for the accuracy with which a random broken line constructed from sums of independent nonidentically distributed random variables can be approximated by a Wiener process. All estimates depend explicitly on the moments of the random variables; meanwhile, these moments can be of a rather general form. In the case of identically distributed random variables we succeed for the first time in constructing an estimate depending explicitly on the common distribution of the summands and directly implying all results of the famous articles by Komlós, Major, and Tusnády which are devoted to estimates in the invariance principle.
Keywords: invariance principle, estimates for the rate of convergence, Komlós–Major–Tusnády estimates, method of the same probability space.
Received: 25.03.2011
English version:
Siberian Mathematical Journal, 2011, Volume 52, Issue 4, Pages 696–710
DOI: https://doi.org/10.1134/S0037446611040136
Bibliographic databases:
Document Type: Article
UDC: 519.214
Language: Russian
Citation: A. I. Sakhanenko, “A general estimate in the invariance principle”, Sibirsk. Mat. Zh., 52:4 (2011), 876–893; Siberian Math. J., 52:4 (2011), 696–710
Citation in format AMSBIB
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\by A.~I.~Sakhanenko
\paper A general estimate in the invariance principle
\jour Sibirsk. Mat. Zh.
\yr 2011
\vol 52
\issue 4
\pages 876--893
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\transl
\jour Siberian Math. J.
\yr 2011
\vol 52
\issue 4
\pages 696--710
\crossref{https://doi.org/10.1134/S0037446611040136}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80051968579}
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  • https://www.mathnet.ru/eng/smj/v52/i4/p876
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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    Abstract page:359
    Full-text PDF :100
    References:54
    First page:2
     
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