Introduction

As explained in the Preface, we study a collection of individuals, each moving among a finite (usually small) number of states. The exact transition times in continuous time form the modelling basis of the phenomena, although often these times are only incompletely observed. The best known example of such incomplete observation is right-censoring in classical survival analysis; here, not all of a set of independent lifetimes are observed, so that for some of them it is only known that they are larger than some specific value. We shall mention other kinds of censoring such as interval-censoring and left-censoring as well as truncation and filtering. Left-truncation in survival analysis means that an individual is included only if its lifetime is larger than some value, whereas by filtering, we mean that the individual is not under observation all the time, but only when a suitable indicator process is switched on.