XII: 15, 134-137, LNM 649 (1978)
LÉPINGLE, Dominique
Une inégalité de martingales (Martingale theory)
The following inequality for a discrete time adapted process $(a_n)$ and its conditional expectations $b_n=E[a_n\,|\,{\cal F}_{n-1}]$ is proved: $$\|(\sum_n b_n^2)^{1/2}\|_1\le 2\|(\sum_n a_n^2)^{1/2}\|_1\ .$$ A similar inequality in $L^p$, $1\!<\!p\!<\!\infty$, does not require adaptedness, and is due to Stein
Keywords: Inequalities, Quadratic variation
Nature: Original
Retrieve article from Numdam

---