Sharp moment estimates for martingales with uniformly bounded square functions

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 kn...

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Veröffentlicht in:	arXiv.org 2021-03
Hauptverfasser:	Stolyarov, Dmitriy, Vasyunin, Vasily, Zatitskiy, Pavel, Zlotnikov, Ilya
Format:	Artikel
Sprache:	eng
Schlagworte:	Estimates Martingales Mathematics - Classical Analysis and ODEs Mathematics - Probability
Online-Zugang:	Volltext
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