Heterogenous Population Dynamical Model: a Filtering Problem

A heterogeneous population of identical particles, divided into a finite number of classes, according to their level of health, is considered. The partition can change during the time and a suitable exchangeability assumption is made, to preserve the property to be identical items of different types. The partition is not observed. We just observe the cardinality of a particular class. The problem of finding the conditional distribution of particles lifetimes, given such observation, is discussed, with stochastic filtering techniques.