Convergence for weighted sums of Lüroth type random variables

Giuliano, Rita; Hadjikyriakou, Milto

doi:10.1016/j.jmaa.2021.125263

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Proof Of Theorem 211

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Cited by 2 publications

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“…Theorem 2.1 is a consequence of the following result, which measures the distance between the characteristic function of 1 R n and γ ; it is a useful trick, which sometimes allows to transfer results proved for variables with density f to the variables of interest (see for instance [13], Theorems 1.1 and 3.5).…”

Section: Proof Of Theorem 21mentioning

confidence: 99%

Convergence results for Oppenheim expansions (II)

Fang

Giuliano

2021

Monatsh Math

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Under the framework of Giuliano (Monatsh Math 187:509-530, 2018) , we continue to study the quantity R n introduced in [11]. The goal of this paper is to find conditions such that R −1 n converges in distribution, n k=1 log R k satisfies the central limit theorem and the large deviation. We cover and expand a number of particular cases in the literature on Oppenheim series and Oppenheim continued fractions.

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Section: Proof Of Theorem 21mentioning

confidence: 99%