Affiliation:
1. Department of Mathematics , Linköping University , Linköping , 58183 , Sweden
2. School of Reliability and Systems Engineering , Beihang University , Beijing , 100083 , P. R. China
Abstract
Abstract
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, 2, 407–428].
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics, Probability and Uncertainty,Mathematical Physics
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