Sharp maximal inequality for nonnegative martingales

Adam Osȩkowski

Statistics & Probability Letters, 2011, vol. 81, issue 12, 1945-1952

Abstract: 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.

Keywords: Martingale; Maximal function; Stochastic integral; Martingale transform (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1016/j.spl.2011.08.009

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