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On the Behavior of the Constant in a Decoupling Inequality for Martingales
Journal article   Open access   Peer reviewed

On the Behavior of the Constant in a Decoupling Inequality for Martingales

Proceedings of the American Mathematical Society, v 121(1), pp 253-258
1994
url
https://doi.org/10.1090/S0002-9939-1994-1176481-2View
Published, Version of Record (VoR) Open

Abstract

Martingales Mathematical constants Mathematical functions Mathematical inequalities Mathematical moments Mathematical sequences Random variables Tangents
Let (fn) and (gn) be two martingales with respect to the same filtration (Fn) such that their difference sequences (dn) and (en) satisfy P(dn≥ λ∣Fn - 1) = P(en≥ λ∣Fn - 1) for all real λ's and n ≥ 1. It is known that$\|f^\ast\|_p \leq K_p\|g^\ast\|_p,\quad 1 \leq p < \infty,$for some constant Kpdepending only on p. We show that Kp= O(p). This will be obtained via a new version of Rosenthal's inequality which generalizes a result of Pinelis and which may be of independent interest.

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