Although Point Processes covers some of the general theory of point processes, that is not its main focus, and it avoids any discussion of statistical inference involving these processes. Instead, its aim is to present the properties and descriptions of several specific processes arising in applications of this theory,[2][3][4][5] which had not been previously collected in texts in this area.[3]
Three of its six chapters concern more general material, while the final three are more specific. The first chapter includes introductory material on standard processes: Poisson point processes, renewal processes, self-exciting processes, and doubly stochastic processes. The second chapter provides some general theory including stationarity, orderliness (meaning that the probability of multiple arrivals in short intervals is sublinear in the interval length), Palm distributions, Fourier analysis, and probability-generating functions.[6] Chapter four (the third of the more general chapters) concerns point process operations, methods of modifying or combining point processes to generate other processes.[5][6]
Chapter three, the first of the three chapters on more specific models, is titled "Special models".[5] The special models that it covers include non-stationary Poisson processes, compound Poisson processes, and the Moran process, along with additional treatment of doubly stochastic processes and renewal processes. Until this point, the book focuses on point processes on the real line (possibly also with a time dimension), but the two final chapters concern multivariate processes and on point processes for higher dimensional spaces, including spatio-temporal processes and Gibbs point processes.[6]
