In this second volume, we set out a general framework for the theory of
point processes, starting from their interpretation as random measures. The
material represents a reorganized version of those parts of Chapters 6–14 of
the first edition not already covered in Volume I, together with a significant
amount of new material.
Contrary to our initial expectations, growth in the theoretical aspects of
the subject has at least matched the growth in applications. Much of the original text has been substantially revised in order to present a more consistent
treatment of marked as well as simple point processes. This applies particularly to the material on stationary processes in Chapter 12, the Palm theory
covered in Chapter 13, and the discussion of martingales and conditional intensities in Chapter 14. Chapter 15, on spatial point processes, has also been
significantly modified and extended. Essentially new sections include Sections 10.3 and 10.4 on point processes defined by Markov chains and Markov
point processes in space; Sections 12.7 on long-range dependence and 12.8 on
scale invariance and self-similarity; Sections 13.4 on marked point processes
and convergence to equilibrium and 13.6 on fractal dimensions; Sections 14.6
on random time changes and 14.7 on Poisson embedding and convergence to
equilibrium; much of the material in Sections 15.1–15.4 on spatial processes
is substantially new or revised; and some recent material on point maps and
point stationarity has been included in Section 13.3.