Sharp maximal inequality for nonnegative martingales

Let X be a nonnegative martingale, let H be a predictable process taking values in [−1,1] and let Y be an Itô integral of H with respect to X. We establish the bound ‖supt≥0|Yt|‖1≤3‖supt≥0Xt‖1 and show that the constant 3 is the best possible.

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Year of publication:	2011
Authors:	Osȩkowski, Adam
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 81.2011, 12, p. 1945-1952
Publisher:	Elsevier
Subject:	Martingale \| Maximal function \| Stochastic integral \| Martingale transform

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011040079