Convergence of ergodic–martingale paraproducts

Vjekoslav Kovač and Mario Stipčić

Statistics & Probability Letters, 2020, vol. 164, issue C

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 Lp-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.

Keywords: Martingale; Ergodic average; Norm convergence; Bilinear operator (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2020.108826

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