Multiple state models for life and other contingencies: the time-discrete approach

Let us assume that a time-continuous Markov model has been assigned. Thus, the transition intensities have been specified and the transition probabilities have been derived. It is self-evident that the implied time-discrete probabilistic structure can be immediately derived. To do this, we simply have to restrict our attention to transition probabilities P_ij (z, t) only, where z, t now denote integer values (actually, the term ‘time-discrete’ typically refers to a scanning of time on an annual or monthly basis).