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2020 Law of the iterated logarithm for a random Dirichlet series
Marco Aymone, Susana Frómeta, Ricardo Misturini
Electron. Commun. Probab. 25(none): 1-14 (2020). DOI: 10.1214/20-ECP340

Abstract

Let $(X_{n})_{n\in \mathds {N}}$ be a sequence of i.i.d. random variables with distribution $\mathbb {P}(X_{1}=1)=\mathbb {P}(X_{1}=-1)=1/2$. Let $F(\sigma )=\sum _{n=1}^{\infty }X_{n}n^{-\sigma }$. We prove that the following holds almost surely \[ \limsup _{\sigma \to 1/2^{+}}\frac {F(\sigma )}{\sqrt {2\mathbb {E} F(\sigma )^{2} \log \log \mathbb {E} F(\sigma )^{2}}}=1. \]

Citation

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Marco Aymone. Susana Frómeta. Ricardo Misturini. "Law of the iterated logarithm for a random Dirichlet series." Electron. Commun. Probab. 25 1 - 14, 2020. https://doi.org/10.1214/20-ECP340

Information

Received: 28 April 2020; Accepted: 22 July 2020; Published: 2020
First available in Project Euclid: 7 August 2020

zbMATH: 07252776
Digital Object Identifier: 10.1214/20-ECP340

Subjects:
Primary: 60G50
Secondary: 11M41

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