Doob Lp maximal inequality
= Doob Lp maximal inequality
{c}
{title2=$L^p$}
{wiki=Doob's_martingale_inequality}
For $p>1$ and a martingale $(M_k)_{k\leq n}$,
$$
\left\|\max_{k\leq n}|M_k|\right\|_p
\leq\frac p{p-1}\|M_n\|_p.
$$
= Doob Lp maximal inequality
{c}
{title2=$L^p$}
{wiki=Doob's_martingale_inequality}
For $p>1$ and a martingale $(M_k)_{k\leq n}$,
$$
\left\|\max_{k\leq n}|M_k|\right\|_p
\leq\frac p{p-1}\|M_n\|_p.
$$