Ergodic Functions That are not Almost Periodic Plus L¹-Mean Zero

2020/02/20 by Jean Carlos Cardozo da Silva, Silva, Jean
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Dynamics and Fractals #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2002.08986

openalex publication_date 2020/02/20 · openalex created_date 2020/03/06 · openalex updated_date 2026/07/28

Abstract

Ergodic Functions are bounded uniformly continuous (BUC) functions that are typical realizations of continuous stationary ergodic process. A natural question is whether such functions are always the sum of an almost periodic with an L¹-mean zero BUC function. The paper answers this question presenting a framework that can provide infinitely many ergodic functions that are not almost periodic plus L¹- mean zero.

Related

• Generalized vector valued almost periodic and ergodic distributions
• Fluctuation of ergodic averages and other stochastic processes
• Proving ergodicity via divergence of ergodic sums
• Mean ergodicity vs weak almost periodicity
• Universally L¹ good sequences with gaps tending to infinity