CONDITIONAL LAW OF LIFETIMES FOR A HETEROGENEOUS POPULATION OF LIVING PARTICLES VIA FILTERING TECHNIQUES

抄録

A model is given for the evolution of a heterogeneous population of identical living particles, divided into different classes. The model is dynamic, since the partition of the population changes as the time goes on. The aim of this paper is to determine the law of the lifetime of each particle given the number of dead particles up to time t. This program is achieved by introducing the occupancy numbers, which are defined as the cardinality of each class. Assuming that the partition is non-observable, a filtering problem arises and the observation coincides with the cardinality of the class of dead particles. A discussion is performed about discrete time approximations of the filter.