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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].
Wydawca
Czasopismo
Rocznik
Tom
Strony
309--314
Opis fizyczny
Bibliogr. 9 poz.
Twórcy
autor
- Department of Mathematics, Linköping University, Linköping, 58183, Sweden
autor
- School of Reliability and Systems Engineering, Beihang University, Beijing, 100083, P. R. China
Bibliografia
- [1] R. C. Bollinger and A. A. Salvia, K-in-a-row failure networks, IEEE Trans. Reliability 31 (1982), 53-56.
- [2] W. O. Bryc, Large deviations by the asymptotic value method, in: Diffusion Processes and Related Problems in Analysis. Vol. I (Evanston 1989), Progr. Probab. 22, Birkhäuser, Boston (1990), 447-472.
- [3] D. Chaing and S. C. Niu, Reliability ofconsecutive k-out-of-n, IEEE Trans. Reliability 30 (1981), 87-89.
- [4] A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, Stoch. Model. Appl. Probab. 38, Springer, Berlin, 2010.
- [5] J. C. Fu, L. Wang and W. Y. W. Lou, On exact and large deviation approximation for the distribution of the longest run in a sequence of two-state Markov dependent trials, J. Appl. Probab. 40 (2003), no. 2, 346-360.
- [6] T. Konstantopoulos, Z. Liu and X. Yang, Laplace transform asymptotics and large deviation principles for longest success runs in Bernoulli trials, J. Appl. Probab. 53 (2016), no. 3, 747-764.
- [7] Z. Liu and X. Yang, A general large deviation principle for longest runs, Statist. Probab. Lett. 110 (2016), 128-132.
- [8] Z. Liu and X. Yang, On the longest runs in Markov chains, Probab. Math. Statist. 38 (2018), no. 2, 407-428.
- [9] Y. Z. Zhang and X. Y. Wu, Some results associated with the longest run in a strongly ergodic Markov chain, Acta Math. Sin. (Engl. Ser.) 29 (2013), no. 10, 1939-1948.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-e4aba5d5-aec9-4f57-8723-b0de1f12d792