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arXiv · 2309.12654

On the Extreme Value Behavior of $\vartheta$-Expansions

Gabriela Ileana Sebe·Dan Lascu·Bilel Selmi
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Abstract

The main objective of this paper is to develop extreme value theory for $\vartheta$-expansions. We establish the limit distribution of the maximum value in a $\vartheta$-continued fraction mixing stationary stochastic process, along with some related results. These findings are analogous to the theorems of J. Galambos and W. Philipp for regular continued fractions. Additionally, we emphasize that a Borel-Bernstein type theorem plays a crucial role.

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Gabriela Ileana Sebe, Dan Lascu, Bilel Selmi. 2023-09-22. On the Extreme Value Behavior of $\vartheta$-Expansions. https://arxiv.org/abs/2309.12654

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