The stochastic processes that we have studied so far all involve data on the times between events. These can be called event histories. The simplest case occurred when there was one type of event and it was absorbing (Chapter 3). The classical examples are human mortality and machine breakdown. The situation is slightly more complex when the event is recurrent (Chapter 4). Examples include unemployment, sickness, and moving house. It is still more complex when individuals may change between distinct states (Chapter 5). Here, an example would be catching a disease, being hospitalised, recovering, or dying. However, up until now, I only have looked at this latter possibility in discrete time, through the use of Markov chains. We shall now see how to generalise those procedures to changes among several states in continuous time.

Theory

When an individual can change state at any point in time in an event history process, each event indicates a transition between states. However, by appropriate definition, it is possible to model almost any series of events, even recurrent events, as a set of transitions among states. I already have covered much of the basic theory in Section 4.1.

Diagrams

With several states and, perhaps, transitions only being possible among some of them, event history processes can be relatively complex. Generally, it is useful to clarify ideas by constructing a diagram for the states and permissible transitions between them. In this light, let us examine several special cases of particular importance:

• Mortality: two states of which the second is absorbing, the classical survival analysis covered in Chapter 3.

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