Osȩkowski, Adam - In: Statistics & Probability Letters 81 (2011) 12, pp. 1945-1952
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.