Geodesic
Kolmogorov's inequality for the maximum of the sum of random variables and its martingale analogues
Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 3, pp. 565-585

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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. 
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     title = {Kolmogorov's inequality for the maximum of the sum of random variables and its martingale analogues},
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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. Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 3, pp. 565-585. http://geodesic.mathdoc.fr/item/TVP_2023_68_3_a7/