XV: 17, 251-258, LNM 850 (1981)
PITMAN, James W.
A note on $L_2$ maximal inequalities (Martingale theory)
This paper contains a $L^2$ inequality between two processes $(X_n,M_n)$ under assumptions which (if $X$ is a martingale) apply to $M_n=\sup_{m\le n} |X_m|$, and to other interesting cases as well. In particular, Doob's inequality is valid for the larger process $\sup_{m\le n} X_m^+ +\sup_{m\le n} X_m^-$
Keywords: Maximal inequality, Doob's inequality
Nature: Original
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