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  • 1.
    Liu, Zhenxia
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Mbokoma, Mainza
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    An improvement on the large deviations for longest runs in Markov chains2023In: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 193, article id 109737Article in journal (Refereed)
    Abstract [en]

    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.

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