A summary of the theory of point processes
Stochastic point processes: statistical analysis, theory, and applications (Conf., IBM Res. Center, Yorktown Heights, N.Y., 1971), Wiley-Interscience, New York, (1972)Zusammenfassung
This extremely well-written review paper will be essential reading for all those contemplating research in the expanding field of stochastic point processes. Because it is a review paper, it is impossible to do much more here than list its contents, which are as follows: 1. Introduction; 2. Basic properties (counting properties, interval properties, finite processes, generalizations); 3. Moment structure and generating functionals; 4. Spectral theory of second order stationary point processes; 5. Operations on point processes (compounding, clustering, random deletions and random shifts, randomization); 6. Orderliness and the intensity measure of a point process; 7. Palm-Hinčin theory; 8. Limit theorems and infinitely divisible point processes.
Naturally, many papers have appeared on this subject since this review paper was published, but particular mention should be made of two recent books viz., S. K. Srinivasa, Stochastic point processes and their applications, Hafner, New York, 1974; J. Kerstan, K. Matthes and J. Mecke, Unbegrenzt teilbare Punkt-prozesse, Akademie-Verlag, Berlin, 1974; English translation to appear.