On the Extreme Value Behavior of ϑ-Expansions

2023/09/22 by Gabriela Ileana Sebe, Sebe, Gabriela Ileana, Dan Lascu +2
Mathematics · Economics, Econometrics and Finance · #Mathematical Dynamics and Fractals #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2309.12654

Abstract

The main objective of this paper is to develop extreme value theory for ϑ-expansions. We establish the limit distribution of the maximum value in a ϑ-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.

Related

• Continued fractions, the Chen-Stein method and extreme value theory
• Extreme Value Laws for non stationary processes generated by sequential and random dynamical systems
• Renewal-type Limit Theorem for Continued Fractions with Even Partial Quotients
• Higher-order expansions of extremes from mixed skew-t distribution
• Regular conditional distributions of max infinitely divisible processes