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., 2023, Volume 68, Issue 3,Pages <nobr>565

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

N. E. Kordzakhia^a, A. A. Novikov^bc, A. N. Shiryaev^c

^a Macquarie University, Sydney, Australia
^b University of Technology Sydney, Sydney, Australia
^c Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

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

DOI: 10.4213/tvp5639