Generalization of tail inequalities for random variables, using in the martingale theory

Abstract

We generalize a famous tail Doob's inequality, relative two non-negative random variables, arising in the martingale theory, in two directions: on the more general source data and on the random variables belonging to the so-called Grand Lebesgue Spaces. We bring also several examples in each sections in order to show the exactness of our estimates.

arXiv commentarXiv admin note: text overlap with arXiv:2206.00537