Some estimates related to the Doob’s martingale inequalities

Milica Jovalekić

Statistics & Probability Letters, 2019, vol. 153, issue C, 124-129

Abstract: Let M be a maximum and let N be a minimum of the non-negative martingale (X1,F1),(X2,F2),…,(Xn,Fn). It is well known (Harremoës, 2008), that if X1=1, then γ(‖M‖1)≤E(XnlogXn)andγ(‖N‖1)≤E(XnlogXn),where γ(x)=x−1−logx, for all x>0. In this paper, we prove the analogue of this result in the case when 10.

Keywords: Doob’s maximal inequalities; Martingales (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2019.05.023

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