Estimation-Calibration of Continuous-Time Non-Homogeneous Markov Chains with Finite State Space

We propose a method for fitting transition intensities to a sufficiently large set of trajectories of a continuous-time non-homogeneous Markov chain with a finite state space. Starting with simulated data computed with Gompertz-Makeham transition intensities, we apply the proposed method to fit piecewise linear intensities and then compare the transition probabilities corresponding to both the Gompertz-Makeham transition intensities and the fitted piecewise linear intensities; the main comparison result is that the order of magnitude of the average fitting error per unit time-chosen as a year-is always less than 1%, thus validating the methodology proposed.