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

Gabriela Ileana Sebe; Dan Lascu; Bilel Selmi

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

Probability 2025-11-04 v2 Number Theory

Authors: Gabriela Ileana Sebe , Dan Lascu , Bilel Selmi

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.

Keywords

extreme value theory theta-expansions continued fractions stationary stochastic process limit distribution borel-bernstein theorem

Cite

@article{arxiv.2309.12654,
  title  = {On the Extreme Value Behavior of $\vartheta$-Expansions},
  author = {Gabriela Ileana Sebe and Dan Lascu and Bilel Selmi},
  journal= {arXiv preprint arXiv:2309.12654},
  year   = {2025}
}

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17 pages

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

Abstract

Keywords

Cite

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