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Maximum likelihood estimator for hidden Markov models in continuous time

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Abstract

The paper studies large sample asymptotic properties of the Maximum Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain, observed in white noise. Using the method of weak convergence of likelihoods due to Ibragimov and Khasminskii (Statistical estimation, vol 16 of Applications of mathematics. Springer-Verlag, New York), consistency, asymptotic normality and convergence of moments are established for MLE under certain strong ergodicity assumptions on the chain.

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Authors and Affiliations

  1. Department of Statistics, The Hebrew University, Mount Scopus, Jerusalem, 91905, Israel

    Pavel Chigansky

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  1. Pavel Chigansky
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Correspondence to Pavel Chigansky.

Additional information

This article has been written during the author’s visit at Laboratoire de Statistique et Processus, Universite du Maine, France, supported by the Chateaubriand fellowship.

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Chigansky, P. Maximum likelihood estimator for hidden Markov models in continuous time. Stat Inference Stoch Process 12, 139–163 (2009). https://doi.org/10.1007/s11203-008-9025-4

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  • DOI: https://doi.org/10.1007/s11203-008-9025-4

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