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Large deviation principle for the backward continued fraction expansion

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  • Takahasi, Hiroki

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.

Suggested Citation

  • Takahasi, Hiroki, 2022. "Large deviation principle for the backward continued fraction expansion," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 153-172.
    • Handle: RePEc:eee:spapps:v:144:y:2022:i:c:p:153-172
    DOI: 10.1016/j.spa.2021.11.002
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    References listed on IDEAS

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    1. Aaronson, Jon & Nakada, Hitoshi, 2003. "Trimmed sums for non-negative, mixing stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 104(2), pages 173-192, April.
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