Burkholder-Davis-Gundy inequalities
= Burkholder-Davis-Gundy inequalities
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For every $p>0$ there are constants $c_p,C_p>0$ such that a continuous local martingale $M$ with $M_0=0$ satisfies
$$
c_p\mathbb E[M]_T^{p/2}\leq\mathbb E\!\left[\sup_{t\leq T}|M_t|^p\right]\leq C_p\mathbb E[M]_T^{p/2}
$$
for every <stopping time> $T$ for which the quantities are finite.
= Burkholder-Davis-Gundy inequality
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{synonym}