Convergence of ergodic-martingale paraproducts
Probability
2020-05-25 v2 Classical Analysis and ODEs
Dynamical Systems
Abstract
In this note we introduce a sequence of bilinear operators that unify ergodic averages and backward martingales in a nontrivial way. We establish its convergence in a range of -norms and leave its a.s. convergence as an open problem. This problem shares some similarities with a well-known unresolved conjecture on a.s. convergence of double ergodic averages with respect to two commuting transformations.
Cite
@article{arxiv.2003.03651,
title = {Convergence of ergodic-martingale paraproducts},
author = {Vjekoslav Kovač and Mario Stipčić},
journal= {arXiv preprint arXiv:2003.03651},
year = {2020}
}
Comments
8 pages; v2: references added and corrected following reviewer's report