Hattendorff’s theorem for non-smooth continuous-time Markov models II: Application

The examples in this second part of our paper illustrate the broad scope of the generalized Hattendorff theorem exposed in Part I as well as some limitations concerning the interpretability of numerical results derived from Hattendorff type theorems. In particular, they show that “mixed” situations in which some transitions of the underlying Markov jump process are governed by smooth cumulative transition intensities, whereas others can only take place at discrete times come up quite naturally. Contrary to previous versions of Hattendorff’s theorem, our result applies to such examples as well as to fully discrete and to fully smooth situations.