We show that bilinear variational estimates of Do, Muscalu, and Thiele  remain valid for a pair of general martingales with respect to the same filtration. Our result can also be viewed as an off-diagonal generalization of the Burkholder–Davis–Gundy inequality for martingale rough paths by Chevyrev and Friz .
"Variational estimates for martingale paraproducts." Electron. Commun. Probab. 24 1 - 14, 2019. https://doi.org/10.1214/19-ECP257