Steven Bradley Lowen & Malvin Carl Teich 
Fractal-Based Point Processes 

An integrated approach to fractals and point processes

This publication provides a complete and integrated presentation of
the fields of fractals and point processes, from definitions and
measures to analysis and estimation. The authors skillfully
demonstrate how fractal-based point processes, established as the
intersection of these two fields, are tremendously useful for
representing and describing a wide variety of diverse phenomena in
the physical and biological sciences. Topics range from
information-packet arrivals on a computer network to
action-potential occurrences in a neural preparation.

The authors begin with concrete and key examples of fractals and
point processes, followed by an introduction to fractals and chaos.
Point processes are defined, and a collection of characterizing
measures are presented. With the concepts of fractals and point
processes thoroughly explored, the authors move on to integrate the
two fields of study. Mathematical formulations for several
important fractal-based point-process families are provided, as
well as an explanation of how various operations modify such
processes. The authors also examine analysis and estimation
techniques suitable for these processes. Finally, computer network
traffic, an important application used to illustrate the various
approaches and models set forth in earlier chapters, is
discussed.

Throughout the presentation, readers are exposed to a number of
important applications that are examined with the aid of a set of
point processes drawn from biological signals and computer network
traffic. Problems are provided at the end of each chapter allowing
readers to put their newfound knowledge into practice, and all
solutions are provided in an appendix. An accompanying Web site
features links to supplementary materials and tools to assist with
data analysis and simulation.

With its focus on applications and numerous solved problem sets,
this is an excellent graduate-level text for courses in such
diverse fields as statistics, physics, engineering, computer
science, psychology, and neuroscience.

Table of Content

Preface.

List of Figures.

List of Tables.

Authors.

1. Introduction.

2. Scaling, Fractals, and Chaos.

3. Point Processes: Definition and Measures.

4. Point Processes: Examples.

5. Fractal and Fractal-Rate Point Processes.

6. Processes Based on Fractional Brownian Motion.

7. Fractal Renewal Processes.

8. Processes Based on the Alternating Fractal Renewal
Process.

9. Fractal Shot Noise.

10. Fractal-Shot-Noise-Driven Point Processes.

11. Operations.

12. Analysis and Estimation.

13. Computer Network Traffic.

Appendix A: Derivations.

Appendix B: Problem Solutions.

Appendix C: List of Symbols.

Bibliography.

Author Index.

Subject Index.

About the author

STEVEN BRADLEY LOWEN, PHD, is Assistant Professor of
Psychiatry at Harvard Medical School and is affiliated with the
Brain Imaging Center at Mc Lean Hospital in Belmont, Massachusetts.
He received a BS degree from Yale University and MS and Ph D degrees
from Columbia University.

MALVIN CARL TEICH, PHD, is Professor in the Departments
of Electrical and Computer Engineering; Biomedical Engineering; and
Physics at Boston University; as well as Professor Emeritus at
Columbia University. He received SB, MS, and Ph D degrees from the
Massachusetts Institute of Technology, Stanford University, and
Cornell University, respectively.