Maximum likelihood estimation of covariates dependent transition intensity of continuous time Markov chains with finite state space

This paper proposes a novel method for maximum likelihood (ML) estimation of transition intensity with covariates dependent of continuous time Markov chains. Score function and observed information matrix of the covariates regression coefficient are presented in explicit forms. In particular, the observed information matrix is positive definite for any values of regression coefficients. This appealing feature of information matrix gives rise to a fast convergence ML recursive estimation of the coefficients. More importantly, to show the consistency and asymptotic normality of the ML estimator. A series of numerical studies confirm the accuracy of the developed results.