Large deviations for longest runs in Markov chains

• Autorzy: Liu Zhenxia , Zhu Yurong

Identyfikatory

DOI

10.1515/jaa-2020-2027

• Języki publikacji: EN

Abstrakty

EN

We continue our investigation on general large deviation principles (LDPs) for longest runs. Previously, a general LDP for the longest success run in a sequence of independent Bernoulli trails was derived in [Z. Liu and X. Yang, A general large deviation principle for longest runs, Statist. Probab. Lett. 110 (2016), 128-132]. In the present note, we establish a general LDP for the longest success run in a two-state (success or failure) Markov chain which recovers the previous result in the aforementioned paper. The main new ingredient is to implement suitable estimates of the distribution function of the longest success run recently established in [Z. Liu and X. Yang, On the longest runs in Markov chains, Probab. Math. Statist. 38 (2018), no. 2, 407-428].

Słowa kluczowe

EN

large deviation principle; Markov chain; longest run

PL

zasada wielkich odchyleń; łańcuch Markowa; najdłuższy przebieg

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2020
• Tom: Vol. 26, nr 2
• Strony: 309--314
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Liu Zhenxia

• Department of Mathematics, Linköping University, Linköping, 58183, Sweden

autor

Zhu Yurong

• School of Reliability and Systems Engineering, Beihang University, Beijing, 100083, P. R. China

Bibliografia

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• [8] Z. Liu and X. Yang, On the longest runs in Markov chains, Probab. Math. Statist. 38 (2018), no. 2, 407-428.
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