Karr A. Point Processes and Their Statistical Inference

2nd Edition. — New York: CRC / Marcel Dekker, Inc., 1991. — 510 p. — ISBN: 0-8247-8532-0Inference for stochastic processes seems to have become a distinct subfield of probability and statistics. No longer viewed as falling between probability and statistics but part of neither, it is now recognized as spanning both.
Questions of inference are current important concerns — not only in classical senses but also in state estimation — for the traditionally important stochastic processes (Markov chains, diffusions, and point processes).
For point processes, progress has been especially rapid because of simple qualitative structure, the wealth of tractable but broad special cases, and, above all, persistent, stimulating contact with applications. This contact provides the impetus for the solution of problems at the same time as, in consonance with most of the history of mathematics, it confirms that important physical problems lead to the most challenging and interesting mathematical questions. Yet as recently as the mid-1970s inference for point processes was more a collection of disparate techniques than a coherent field of scientific investigation. The introduction of martingale methods for statistical estimation, hypothesis testing, and state estimation revolutionized the then inchoate field, at once expanding the family of models amenable to meaningful analysis and unifying, albeit conceptually more than practically, the
entire subject. Developments since then have been numerous and diverse, but without engendering fragmentation.
The goal of this book is to present a unified (but necessarily, of course, incomplete) description of inference for point processes before the field becomes so broad that such a goal is hopeless. By depicting the probabilistic and statistical heart of the subject, as well as several of its boundaries, I have endeavored to convey simultaneously the unity and diversity whose interplay and tension I find so alluring.