TY - JOUR
AU - Formica, Maria Rosaria
AU - Ostrovsky, Eugeny
AU - Sirota, Leonid
PY - 2022/10/12
Y2 - 2024/08/04
TI - Generalization of Tail Inequalities for Random Variables in the Martingale Theory
JF - Contemporary Mathematics
JA - Contemp. Math.
VL - 3
IS - 4
SE - Research Article
DO - 10.37256/cm.3420221587
UR - https://ojs.wiserpub.com/index.php/CM/article/view/1587
SP - 457-467
AB - <p>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.</p>
ER -