Convergence of series of strongly integrable random variables and applications

Boukhari, Fakhreddine; Malti, Dounyazed

doi:10.1016/j.spl.2018.01.029

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Weighted Strong Law Of Large Numbers1

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Cited by 3 publications

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“…We point out that in all proved results the independence of the random variables {f n } is not required. In [10] the a.e. convergence of the series of admissible random variables in Orlicz spaces has been investigated.…”

Section: Weighted Strong Law Of Large Numbersmentioning

confidence: 99%

Weighted Laws of Large Numbers and Weighted One-Sided ergodic Hilbert Transforms on Vector Valued $L_p$-spaces

Mukhamedov¹

2020

Preprint

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A more general notion of weight called admissible is introduced and then an investigation is carried out on the a.e. convergence of weighted strong laws of large numbers and their applications to weighted one-sided ergodic Hilbert transforms on vector-valued Lp-spaces. Furthermore, the obtained results are applied to the a.e. convergence of random modulated weighted ergodic series, which is also new in the classical setting.

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Section: Weighted Strong Law Of Large Numbersmentioning

confidence: 99%