Large deviations for random dynamical systems and applications to hidden Markov models |
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Authors: | Shulan Hu |
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Affiliation: | a Department of Statistics, Zhongnan University of Economics and Law, 430073 Hubei, Chinab Laboratoire de Mathématiques Appliquées, CNRS-UMR 6620, Université Blaise Pascal, 63177 Aubière, Francec Institute of Applied Mathematics, Chinese Academy of Sciences, 100190 Beijing, China |
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Abstract: | In this paper, we prove the large deviation principle (LDP) for the occupation measures of not necessarily irreducible random dynamical systems driven by Markov processes. The LDP for not necessarily irreducible dynamical systems driven by i.i.d. sequence is derived. As a further application we establish the LDP for extended hidden Markov models, filling a gap in the literature, and obtain large deviation estimations for the log-likelihood process and maximum likelihood estimator of hidden Markov models. |
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Keywords: | 60F10 |
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