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

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

Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 3, pp. 565-585

Résumé

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.

Détail

Keywords: maximal inequality, Kolmogorov inequality, Doob inequality, stopping time, moment martingale identities, exponential martingale identity.

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