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

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  • Cuny, Christophe
  • Fan, Ai Hua

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 Gapošhkin (1967) (see also Gapošhkin (1968)). Applications are also given to the almost everywhere convergence with respect to Riesz products of lacunary series.

Suggested Citation

  • Cuny, Christophe & Fan, Ai Hua, 2017. "Study of almost everywhere convergence of series by mean of martingale methods," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2725-2750.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:8:p:2725-2750
    DOI: 10.1016/j.spa.2016.12.006
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    References listed on IDEAS

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    1. Volný, Dalibor, 1993. "Approximating martingales and the central limit theorem for strictly stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 44(1), pages 41-74, January.
    2. Hannan, E. J., 1979. "The central limit theorem for time series regression," Stochastic Processes and their Applications, Elsevier, vol. 9(3), pages 281-289, December.
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