Weak continuity of predictive distribution for Markov survival processes

We explore the concept of a consistent exchangeable survival process - a joint distribution of survival times in which the risk set evolves as a continuous-time Markov process with homogeneous transition rates. We show a correspondence with the de Finetti approach of constructing an exchangeable survival process by generating iid survival times conditional on a completely independent hazard measure. We describe several specific processes, showing how the number of blocks of tied failure times grows asymptotically with the number of individuals in each case. In particular, we show that the set of Markov survival processes with weakly continuous predictive distributions can be characterized by a two-dimensional family called the harmonic process. We end by applying these methods to data, showing how they can be easily extended to handle censoring.