Moving averages of ergodic processes

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1977 Germany English Publisher:Springer Science and Business Media LLCJournal:Metrika, volume 24, pages 35-43 (issn: 0026-1335, eissn: 1435-926X,

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Authors: Junco, A. del; Steele, J.M.;

doi: 10.1007/bf01893390

Moving averages of ergodic processes

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Abstract

A necessary and sufficient condition for the almost everywhere convergence of the “moving” ergodic averages\((\Phi (n))^{ - 1} \mathop \Sigma \limits_{i = n - \Phi (n) + 1}^n x_E (T^i x)\) is given. The result is then generalized to ergodic flows, and finally constrasted with earlier results ofPfaffelhuber andJain.

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Germany

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Keywords

510.mathematics, Measure-preserving transformations, Article, Ergodic theory of linear operators

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