The Kolmogorov inequality for the maximum of the sum of random variables and its martingale analogues

N. E. Kordzakhia; A. A. Novikov; A. N. Shiryaev

doi:10.1137/S0040585X97T991568

The Kolmogorov inequality for the maximum of the sum of random variables and its martingale analogues

N. E. Kordzakhia, A. A. Novikov, A. N. Shiryaev

School of Mathematical and Physical Sciences

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	457-472
Number of pages	16
Journal	Theory of Probability and its Applications
Volume	68
Issue number	3
DOIs	https://doi.org/10.1137/S0040585X97T991568
Publication status	Published - 2023

Keywords

Doob inequality
exponential martingale identity
Kolmogorov inequality
maximal inequality
moment martingale identities
stopping time

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10.1137/S0040585X97T991568

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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 = "Doob inequality, exponential martingale identity, Kolmogorov inequality, maximal inequality, moment martingale identities, stopping time",

author = "Kordzakhia, {N. E.} and Novikov, {A. A.} and Shiryaev, {A. N.}",

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AU - Kordzakhia, N. E.

AU - Novikov, A. A.

AU - Shiryaev, A. N.

PY - 2023

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KW - Doob inequality

KW - exponential martingale identity

KW - Kolmogorov inequality

KW - maximal inequality

KW - moment martingale identities

KW - stopping time

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JO - Theory of Probability and its Applications

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ER -

The Kolmogorov inequality for the maximum of the sum of random variables and its martingale analogues

Abstract

Keywords

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