Likelihood inference for discretely observed Markov jump processes with finite state space is investigated. The existence and uniqueness of the maximum likelihood estimator of the intensity matrix are investigated. This topic is closely related to the imbedding problem for Markov chains. It is...

The paper demonstrates how discrete time credit rating data (e.g. annual observations) can be analysed by means of a continuous-time Markov model. Two methods for estimating the transition intensities are given: the EM algorithm and an MCMC approach. The estimated transition intensities can be...

We study the structure of point processes N with the property that the vary in a finite-dimensional space where [theta]t is the shift and the [sigma]-field generated by the counting process up to time t. This class of point processes is strictly larger than Neuts' class of Markovian arrival...

We consider a multidimensional diffusion X with drift coefficient b(Xt,[alpha]) and diffusion coefficient [epsilon]a(Xt,[beta]) where [alpha] and [beta] are two unknown parameters, while [epsilon] is known. For a high frequency sample of observations of the diffusion at the time points k/n,...

A new general approach to constructing a quasi score function for a class of stochastic processes is proposed. A crucial point in the construction is the separate treatment of the continuous martingale part and the purely discontinuous martingale part. The proposed estimating function fits into...