We consider the mixed dicrete-continuous pattern of observation in a multi-state model; this is a classical pattern because very often clinical status is assessed at discrete visit times while time of death is observed exactly. The likelihood can easily be written heuristically for such models. However a formal proof is not easy in such observational patterns. We give a rigorous derivation al the likelihood for the illness-death model based on applying Jacod´s formula to an observed bivariate counting...

Let ${(X_t,Y_t)}_{t\in 𝕋}$ be a discrete or continuous-time Markov process with state space $𝕏\times {ℝ}^d$ where $𝕏$ is an arbitrary measurable set. Its transition semigroup is assumed to be additive with respect to the second component, i.e. ${(X_t,Y_t)}_{t\in 𝕋}$ is assumed to be a Markov additive process. In particular, this implies that the first component ${\left(X_t\right)}_{t\in 𝕋}$ is also a Markov process. Markov random walks or additive functionals of a Markov process are special instances of Markov additive processes. In this paper, the process ${\left(Y_t\right)}_{t\in 𝕋}$ is shown to satisfy the...