Sharp moment estimates for martingales with uniformly bounded square functions
| Autor: | Stolyarov, Dmitriy, Vasyunin, Vasily, Zatitskiy, Pavel, Zlotnikov, Ilya |
|---|---|
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Mathematische Zeitschrift, Volume 302, Issue 1, (2022), 181--217 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00209-022-03064-x |
| Popis: | We provide sharp bounds for the exponential moments and $p$-moments, $1\leqslant p \leqslant 2$, of the terminate distribution of a martingale whose square function is uniformly bounded by one. We introduce a Bellman function for the corresponding extremal problem and reduce it to the already known Bellman function on $\mathrm{BMO}([0,1])$. In the case of tail estimates, a similar reduction does not work exactly, so we come up with a fine supersolution that leads to sharp tail estimates. Comment: 33 pages, 4 figures; second version corrects some typos |
| Databáze: | arXiv |
| Externí odkaz: |
|