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.
| Original language | English |
|---|---|
| Pages (from-to) | 457-467 |
| Number of pages | 11 |
| Journal | Contemporary Mathematics (Singapore) |
| Volume | 3 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2022 |
Bibliographical note
Publisher Copyright:© 2022 Maria Rosaria Formica, et al.
Funding
M.R. Formica is partially supported by University of Naples “Parthenope”, Dept. of Economic and Legal Studies, project CoRNDiS, DM MUR 737/2021, CUP I55F21003620001. M.R. Formica is member of Gruppo Nazionale per l’Analisi Matematica, la Probabilit`a e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and member of the UMI group “Teoria dell’Approssimazione e Applicazioni (T.A.A.)”.
| Funders | Funder number |
|---|---|
| Teoria dell’Approssimazione e Applicazioni | |
| Università degli Studi di Napoli Federico II | DM MUR 737/2021, CUP I55F21003620001 |
| Istituto Nazionale di Alta Matematica "Francesco Severi" | |
| Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni |
Keywords
- Doob’s inequalities
- Grand Lebesgue spaces
- Young-Fenchel transform
- expectation
- martingale
- probability space
- random variable
- tail of distribution