Point Process Calculus in Time and Space

This book provides an introduction to the theory and applications of point processes, both in time and in space. Presenting the two components of point process calculus, the martingale calculus and the Palm calculus, it aims to develop the computational skills needed for the study of stochastic models involving point processes, providing enough of the general theory for the reader to reach a technical level sufficient for most applications.

Classical and not-so-classical models are examined in detail, including PoissonCox, renewal, cluster and branching (KerstanHawkes) point processes.The applications covered in this text (queueing, information theory, stochastic geometry and signal analysis) have been chosen not only for their intrinsic interest but also because they illustrate the theory.

Written in a rigorous but not overly abstract style, the book will be accessible to earnest beginners with a basic training in probability but will also interest upper graduate students and experienced researchers.

Addresses both beginners and more experienced probabilists using a rigorous mathematical treatment in a convivial style Provides the theoretical details, yet is oriented toward applications Covers both spatial point processes and point processes on the line

Autorentext

Pierre Brémaud is an Emeritus Professor of the École polytechnique fédérale de Lausanne and alumnus of the École Polytechnique in France. He obtained his Doctorate in Mathematics from the University of Paris VI and his PhD from the department of Electrical Engineering and Computer Science of the University of California at Berkeley. He is a major contributor to the theory of stochastic processes and their applications, and has authored or co-authored several reference and textbooks on the subject.

Inhalt

Introduction.- Generalities.- Poisson Process on the Line.- Spatial Poisson Processes.- Renewal and Regenerative Processes.- Point Processes with a Stochastic Intensity.- Exvisible Intensity of Finite Point Processes.- Palm Probability on the Line.- Palm Probability in Space.- The Power Spectral Measure.- Information Content of Point Processes.- Point Processes in Queueing.- Hawkes Point Processes.- Appendices.- Bibliography.- Index.