Analysis Seminar: Predictable Subordination, Sharp Martingale Estimates and Applications

Abstract: We introduce a new method for obtaining sharp martingale inequalities under predictable analogues of differential subordination, thereby weakening the classical hypothesis introduced by Burkholder in the 1980s. The main idea is to treat simultaneously the continuous and jump contributions arising from the relevant Bellman function, rather than estimating them separately. This principle is flexible and applies to a broad class of Bellman-function arguments. As an application, we combine the resulting martingale inequalities with martingale representations of Riesz transforms to obtain improved bounds in settings not covered by classical differential subordination.

Faculty Host: Alan Chang