The Gundy-Stein decomposition with explicit constants

Mahdi Hormozi, Jie-Xiang Zhu

Let $({\mathcal{F}}_n{)}_{n\ge 1}$ be a filtration and let $f\ge 0$ belong to $L^1({\mathcal{F}}_{\infty })$. For the martingale $f_n=\mathbb{E}[f\mid {\mathcal{F}}_n]$ and each $\lambda >0$ we prove a G…