Simple and Marked Point Processes

Abstracts

This chapter contains the definitions of simple and marked point processes (SPPs and MPPs, respectively) recording the random occurrences over time of random events and shows how to identify the point processes with counting processes (CPs) and random counting measures (RCMs). The canonical spaces K, and K_E of sequences of time-points of events and their marks are introduced together with the space W of counting process paths and the space M of discrete counting measures, counting timepoints and marks. It is demonstrated how SPPs and MPPs may be viewed as random variables with values in the sequence spaces K and K_E respectively, while CPs are W-valued and RCMs are M-valued random variables. The definitions and notation given in the chapter are fundamental for everything that follows.