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Teoriya Veroyatnostei i ee Primeneniya, 2023, Volume 68, Issue 3, Pages 565–585
DOI: https://doi.org/10.4213/tvp5639 (Mi tvp5639) 		 
Kolmogorov's inequality for the maximum of the sum of random variables and its martingale analogues

N. E. Kordzakhiaa, A. A. Novikovbc, A. N. Shiryaevc

a Macquarie University, Sydney, Australia
b University of Technology Sydney, Sydney, Australia
c Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
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DOI: https://doi.org/10.4213/tvp5639
Abstract: We give a survey of the results related to extensions of the Kolmogorov inequality for the distribution of the absolute value of the maximum of the sum of centered independent random variables to the case of martingales considered at random stopping times.
Keywords: maximal inequality, Kolmogorov inequality, Doob inequality, stopping time, moment martingale identities, exponential martingale identity.
Received: 16.05.2023
Accepted: 03.07.2023
English version:
Theory of Probability and its Applications, 2023, Volume 68, Issue 3, Pages 457–472
DOI: https://doi.org/10.1137/S0040585X97T991568
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: N. E. Kordzakhia, A. A. Novikov, A. N. Shiryaev, “Kolmogorov's inequality for the maximum of the sum of random variables and its martingale analogues”, Teor. Veroyatnost. i Primenen., 68:3 (2023), 565–585; Theory Probab. Appl., 68:3 (2023), 457–472
Citation in format AMSBIB
\Bibitem{KorNovShi23}
\by N.~E.~Kordzakhia, A.~A.~Novikov, A.~N.~Shiryaev
\paper Kolmogorov's inequality for the maximum of the sum of random variables and its martingale analogues
\jour Teor. Veroyatnost. i Primenen.
\yr 2023
\vol 68
\issue 3
\pages 565--585
\mathnet{http://mi.mathnet.ru/tvp5639}
\crossref{https://doi.org/10.4213/tvp5639}
\transl
\jour Theory Probab. Appl.
\yr 2023
\vol 68
\issue 3
\pages 457--472
\crossref{https://doi.org/10.1137/S0040585X97T991568}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85179372683}
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