An introduction to the theory of point processes. Vol. I: Elementary theory and methods. 2nd ed.

*(English)*Zbl 1026.60061
Probability and Its Applications. New York, NY: Springer. xxi, 469 p. (2003).

The second edition of this monograph is divided into two volumes. The first one is concentrated on introductory material and models, the second one on structure and general theory. The original aim to present a broad introduction to the theory of point processes remained unchanged. Since the first edition (1988; Zbl 0657.60069) theory and applications of point processes have been developed rapidly. As for as it was possible under the mentioned aim, the authors take into account this progress.

This first volume includes eight chapters and three appendices. The first five chapters have been changed only a few in comparison with the first edition. The main changes concern the Chapters 6-8, entitled now as follows: 6. Models constructed via conditioning: Cox, cluster, and marked point processes, 7. Conditional intensities and likelihoods, 8. Second-order properties of stationary point processes. Chapter 7 includes links to simulation and prediction algorithms for point processes. The three Appendices of the first edition are included in the first volume of this edition. They concern topology and measure theory; measures on metric spaces as well as conditional expectations, stopping times and martingales.

The second edition of the first volume is an updated and extended introduction to point processes suitable as a textbook with many exercises for beginners as well as a source for scientists interesting in high level applications of point processes.

This first volume includes eight chapters and three appendices. The first five chapters have been changed only a few in comparison with the first edition. The main changes concern the Chapters 6-8, entitled now as follows: 6. Models constructed via conditioning: Cox, cluster, and marked point processes, 7. Conditional intensities and likelihoods, 8. Second-order properties of stationary point processes. Chapter 7 includes links to simulation and prediction algorithms for point processes. The three Appendices of the first edition are included in the first volume of this edition. They concern topology and measure theory; measures on metric spaces as well as conditional expectations, stopping times and martingales.

The second edition of the first volume is an updated and extended introduction to point processes suitable as a textbook with many exercises for beginners as well as a source for scientists interesting in high level applications of point processes.

Reviewer: Uwe Küchler (Berlin)

##### MSC:

60G55 | Point processes (e.g., Poisson, Cox, Hawkes processes) |

60-02 | Research exposition (monographs, survey articles) pertaining to probability theory |

60G57 | Random measures |