Large deviation principle for the backward continued fraction expansion

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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.

Original languageEnglish
Pages (from-to)153-172
Number of pages20
JournalStochastic Processes and their Applications
Volume144
DOIs
Publication statusPublished - 2022 Feb

Keywords

  • Backward continued fractions
  • Large deviation principle
  • Multifractal analysis
  • Thermodynamic formalism

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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