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Teoriya Veroyatnostei i ee Primeneniya, 2020, Volume 65, Issue 4, Pages 778–804
DOI: https://doi.org/10.4213/tvp5295 (Mi tvp5295) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Prokhorov distance with rates of convergence under sublinear expectations

Q. Zhoua, A. I. Sakhanenkoba, J. Guoa

a School of Mathematical Sciences, Nankai University, Tianjin, P.R. China
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
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DOI: https://doi.org/10.4213/tvp5295
Abstract: Prokhorov distances under sublinear expectations are presented in the CLT and the functional CLT, and the convergence rates for them are obtained by the Lindeberg method. In particular, the obtained estimate in the functional CLT yields the known Borovkov estimate in the classical functional CLT with an explicit constant.
Keywords: sublinear expectation, Prokhorov distance, Lindeberg method.
Funding agency Grant number
National Natural Science Foundation of China 11931018
Russian Academy of Sciences - Federal Agency for Scientific Organizations 0314-2019-0008
Russian Foundation for Basic Research 20-51-12007
Natural Science Foundation of Tianjin Province
This work was supported by NSFC (Grant № 11931018) and Tianjin NSF. The research of the second author was also supported by RFBR (Grant № 20-51-12007) and by the program of fundamental scientific researches of the SB RAS № I.1.3 (Project № 0314-2019-0008).
Received: 16.02.2019
Revised: 15.09.2019
Accepted: 17.09.2019
English version:
Theory of Probability and its Applications, 2021, Volume 65, Issue 4, Pages 616–638
DOI: https://doi.org/10.1137/S0040585X97T990150
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Q. Zhou, A. I. Sakhanenko, J. Guo, “Prokhorov distance with rates of convergence under sublinear expectations”, Teor. Veroyatnost. i Primenen., 65:4 (2020), 778–804; Theory Probab. Appl., 65:4 (2021), 616–638
Citation in format AMSBIB
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\by Q.~Zhou, A.~I.~Sakhanenko, J.~Guo
\paper Prokhorov distance with rates of convergence under sublinear expectations
\jour Teor. Veroyatnost. i Primenen.
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\vol 65
\issue 4
\pages 778--804
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\crossref{https://doi.org/10.4213/tvp5295}
\transl
\jour Theory Probab. Appl.
\yr 2021
\vol 65
\issue 4
\pages 616--638
\crossref{https://doi.org/10.1137/S0040585X97T990150}
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  • https://doi.org/10.4213/tvp5295
  • https://www.mathnet.ru/eng/tvp/v65/i4/p778
    • This publication is cited in the following 1 articles:
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