Some remarks on Davis inequality for biparameter filtrations
Abstract
The Davis inequality E Sf E f* between L1 norms of square function of a martingale and its maximal function is known for martingales indexed by linearly ordered filtrations and in some particular cases for double indexed one. We prove the inequality for arbitrary filtrations satisfying the (F4) condition of Cairoli and Walsh and propose a method to attack the other inequality. The former is done by means of a two-parameter analogue of Davis-Garsia decomposition.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.