Large deviation principle for the backward continued fraction expansion

Hiroki Takahasi

Stochastic Processes and their Applications, 2022, vol. 144, issue C, 153-172

Abstract: We investigate stochastic properties of the backward continued fraction expansion of irrational numbers in (0,1). For the mean process associated with a real-valued observable which depends only on the first digit of the expansion, we establish the large deviation principle. For any such observable which is non-negative, we completely determine the set of minimizers of the rate function in terms of a growth rate of the observable. Our method of proof employs the thermodynamic formalism for topological Markov shifts, and a multifractal analysis of pointwise Lyapunov exponents for the Rényi map generating the backward continued fraction expansion.

Keywords: Backward continued fractions; Large deviation principle; Thermodynamic formalism; Multifractal analysis (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2021.11.002

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