A Course on Point Processes

Chapters 1 and 2 of this book originated from a manuscript that was dis­ tributed shortly before aseminar. Each of the participants had acquired a solid background in probability theory and statistics, yet the knowledge of point or counting processes was partly restricted to the homogeneous Poisson counting process buHt by partial sums of exponential random vari­ ables. These preparations turned out to be successful and, consequently, there was time left during the seminar to study some of the topics outlined in Chapters 3-9. This story reveals the main intention of writing this book, namely, to facilitate first steps into the field of point processes. To avoid misunderstanding, this book is not written in an informal style but in strictly mathematical terms. The book provides extensive explana­ tions and detailed proofs (including the discussion of measurability prob­ lems, etc.) which will be helpful to gain insight on the subject. Although this book is of an introductionary nature it includes much new material and presents an elaboration of various topics in a way that cannot be found elsewhere. A broader knowledge and deeper understanding of the subject may be gained by consulting well-known monographs such as those of Daley and Vere-Jones [36], Resnick [128], Matthes, Kerstan and Mecke [104], Karr [88], Kallenberg [87], among others, as weH as originalliterature. For that enterprise, introductory remarks about various specific topics and extensive references may serve as a guideline.