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Journal Articles Stochastic Processes and their Applications Year : 2017

Study of almost everywhere convergence of series by mean of martingale methods

Abstract

Martingale methods are used to study the almost everywhere convergence of general function series. Applications are given to ergodic series, which improves recent results of Fan (2015), and to dilated series, including Davenport series, which completes results of Gaposhkin (1967) (see also Gaposhkin (1968)). Applications are also given to the almost everywhere convergence with respect to Riesz products of lacunary series. (C) 2016 Elsevier B.V. All rights reserved.

Dates and versions

hal-02404277 , version 1 (11-12-2019)

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Christophe Cuny, Ai Hua Fan. Study of almost everywhere convergence of series by mean of martingale methods. Stochastic Processes and their Applications, 2017, 127 (8), pp.2725-2750. ⟨10.1016/j.spa.2016.12.006⟩. ⟨hal-02404277⟩
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