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An improvement on the large deviations for longest runs in Markov chains

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  • Liu, Zhenxia
  • Mbokoma, Mainza

Abstract

Large deviations for longest success runs L(n) in Markov chains have been previously studied in Liu and Yang (2018) and Liu and Zhu (2020) under a technical assumption p10≤p00+p11, with pij denoting the transition probability from i to j. In this note, we prove that all the results in Liu and Yang (2018) and Liu and Zhu (2020) still hold even without such an assumption. The main step in the proof is to derive an improved global estimation for the distribution function of L(n) without this assumption, which might be of independent interest.

Suggested Citation

  • Liu, Zhenxia & Mbokoma, Mainza, 2023. "An improvement on the large deviations for longest runs in Markov chains," Statistics & Probability Letters, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:stapro:v:193:y:2023:i:c:s0167715222002504
    DOI: 10.1016/j.spl.2022.109737
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    References listed on IDEAS

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    1. Liu, Zhenxia & Yang, Xiangfeng, 2016. "A general large deviation principle for longest runs," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 128-132.
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