Variational estimates for martingale paraproducts
arXiv:1812.09763 · doi:10.1214/19-ECP257
Abstract
We show that bilinear variational estimates of Do, Muscalu, and Thiele (arXiv:1009.5187) 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 (arXiv:1704.08053).
13 pages, implications for continuous time martingales discussed in more detail