Generalization of Tail Inequalities for Random Variables in the Martingale Theory

Authors

  • Maria Rosaria Formica Parthenope University of Naples, via Generale Parisi 13, Naples, Italy https://orcid.org/0000-0003-3962-9554
  • Eugeny Ostrovsky Bar-Ilan University, Department of Mathematics and Statistics, Ramat Gan, Israel
  • Leonid Sirota Bar-Ilan University, Department of Mathematics and Statistics, Ramat Gan, Israel

DOI:

https://doi.org/10.37256/cm.3420221587

Keywords:

martingale, random variable, expectation, tail of distribution, probability space, Doob's inequality, Grand Lebesgue spaces, Young-Fenchel transform

Abstract

We generalize the tail Doob's inequality, concerning two non-negative random variables, arising in the martingale theory, in three directions: on the more general source data, on the random variables belonging to the so-called Grand Lebesgue Spaces, as well as on the multidimensional variables. We also provide several examples. Moreover we show the exactness of the estimates obtained in the particular case of positive random variables having exponential distribution.

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Published

2022-10-12

How to Cite

1.
Formica MR, Ostrovsky E, Sirota L. Generalization of Tail Inequalities for Random Variables in the Martingale Theory. Contemp. Math. [Internet]. 2022 Oct. 12 [cited 2024 Jul. 18];3(4):457-6. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/1587