Special Classes of Processes

We have already discussed in Volume I a variety of particular models for point processes and random measures, and described many of their properties. With the added benefit of the basic theory in Chapter 9, we return here to the study of four important classes of models: completely random measures; infinitely divisible point processes; point processes generated by Markov chains; and Markov point processes in space. Each class has interest in its own right, and contains models which are widely used in applications. Although it is the intrinsic interest of the models that motivates the discourse, our immediate aims are to use the theory of the last chapter to establish structure theorems for these classes, to show that they are well-defined mathematical objects, and to establish some of their general properties.