Fractals are well-known mathematical objects (usually represented geometrically) that have the property of self-similarity at different scales. They may also be described as having noninteger dimensions (or technically, by saying that their Hausdorff dimensions are greater than their topological dimensions). Most people with an interest in math and science are familiar with examples of fractals such as the Mandelbrot set and the Koch snowflake, and fractals have been discussed by such eminent authors as Stephen Jay Gould [1] and Roger Penrose [2].

Point processes are records of the occurrences of stochastic events over a period of time. There are two basic types of point processes: the counting process, which follows the number of events in a fixed period of time, and the interval process, which considers the intervals between consecutively occurring events.

This book is, as its title suggests, a study of point processes that have fractal characteristics. It is a very well-written monograph on its subject, which it covers from the basics to the advanced topics, and includes problems at the end of each chapter (and solutions in Appendix B), making it an excellent resource for instructors and students. There is also an accompanying Web site by one of the authors (Lowen), featuring such things as errata, addenda, and C source code. The book also features what appears to be a comprehensively researched bibliography (even on secondary topics, such as competing theories about power-law behaviors in systems) that researchers will surely appreciate.

The first chapter provides an introduction in a nutshell to fractals and point processes. Chapter 2 discusses the questions of scaling and dimensions in fractals, and correlates fractals and chaos (which are related but not identical, though they are confounded often in popular writings). The third and fourth chapters introduce point processes in a little more detail, and also give examples of them. Chapter 5 builds on the earlier material to present fractal and fractal-rate point processes. The next five chapters present advanced topics such as Brownian motion and various types of noise. Chapter 11 presents operations on point processes (such as dilation, deletion, and displacement) and their applications in the relevant context. Chapter 12 discusses tools for their analysis and estimation. Chapter 13 is the one most likely to be of interest to a computer science/information technology audience, as it discusses the application of the theory presented to the analysis of data traffic on computer networks, which are well known for their fractal characteristics. Appendix A presents mathematical derivations (sensibly postponed so as to avoid interfering with the flow of the discussion), while Appendix B contains solutions to problems previously given.

The book assumes an in-depth understanding of statistics, as well as some significant background in functional analysis (including the theory of wavelets). Therefore, it will not be readily accessible to readers lacking this knowledge.