Maximum Likelihood Estimator for Hidden Markov Models in continuous time

TL;DR

This paper analyzes the large sample properties of the MLE for continuous-time Markov chains observed in white noise, establishing consistency, asymptotic normality, and moment convergence under ergodicity conditions.

Contribution

It extends the theoretical understanding of MLE behavior for continuous-time Markov chains in noisy observations, using weak convergence methods.

Findings

MLE is consistent under ergodicity.

MLE is asymptotically normal.

Convergence of moments is proven.

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 I.Ibragimov and R.Khasminskii, consistency, asymptotic normality and convergence of moments are established for MLE under certain strong ergodicity conditions of the chain.