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Teoriya Veroyatnostei i ee Primeneniya, 1997, Volume 42, Issue 2, Pages 239–261
DOI: https://doi.org/10.4213/tvp1801 (Mi tvp1801) 		 
This article is cited in 8 scientific papers (total in 8 papers)

To the invariance principle

V. M. Kruglov

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
Full-text PDF (1123 kB) Citations (8)
DOI: https://doi.org/10.4213/tvp1801
Abstract: Five functionals of the sums of independent random variables are discussed. The asymptotic analysis of these functionals played an important role in the development of the invariance principle. It is demonstrated that the weak convergence of each of these appropriately generalized functionals is equivalent to the applicability of the central limit theorem to sums of random variables on the basis of which the functionals are constructed.
Keywords: independent random variables, random broken line, process of Brownian motion, limit theorems for functionals of random variables.
Received: 16.06.1995
English version:
Theory of Probability and its Applications, 1998, Volume 42, Issue 2, Pages 225–243
DOI: https://doi.org/10.1137/S0040585X9797609X
Bibliographic databases:
Language: Russian
Citation: V. M. Kruglov, “To the invariance principle”, Teor. Veroyatnost. i Primenen., 42:2 (1997), 239–261; Theory Probab. Appl., 42:2 (1998), 225–243
Citation in format AMSBIB
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\paper To the invariance principle
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\transl
\jour Theory Probab. Appl.
\yr 1998
\vol 42
\issue 2
\pages 225--243
\crossref{https://doi.org/10.1137/S0040585X9797609X}
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  • https://doi.org/10.4213/tvp1801
  • https://www.mathnet.ru/eng/tvp/v42/i2/p239
    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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