We present a new proof of the Burkholder–Davis–Gundy inequalities for $1\leq p<\infty$. The novelty of our method is that these martingale inequalities are obtained as consequences of elementary deterministic counterparts. The latter have a natural interpretation in terms of robust hedging.
"Pathwise versions of the Burkholder–Davis–Gundy inequality." Bernoulli 21 (1) 360 - 373, February 2015. https://doi.org/10.3150/13-BEJ570