Continued fractions, the Chen-Stein method and extreme value theory

Article Type

Research Article

Publication Title

Ergodic Theory and Dynamical Systems

Abstract

In this work we deal with extreme value theory in the context of continued fractions using techniques from probability theory, ergodic theory and real analysis. We give an upper bound for the rate of convergence in the Doeblin-Iosifescu asymptotics for the exceedances of digits obtained from the regular continued fraction expansion of a number chosen randomly from (0, 1) according to the Gauss measure. As a consequence, we significantly improve the best known upper bound on the rate of convergence of the maxima in this case. We observe that the asymptotics of order statistics and the extremal point process can also be investigated using our methods.

First Page

461

Last Page

470

DOI

10.1017/etds.2019.64

Publication Date

2-1-2021

Comments

Open Access, Green

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