Point Process Calculus in Time and Space: An Introduction with Applications

This book provides an introduction to the theory and applications of point processes, covering classical and not-so-classical models, and illustrating their applications in queueing, information theory, stochastic geometry, and signal analysis. It is written in a rigorous but not overly abstract style and will be accessible to earnest beginners and upper graduate students.

Format: Paperback / softback
Length: 556 pages
Publication date: 07 December 2021
Publisher: Springer Nature Switzerland AG

This comprehensive book delves into the realm of point processes, offering a thorough introduction to both their theoretical foundations and practical applications. It begins by presenting the fundamental concepts of point process calculus, encompassing the martingale calculus and Palm calculus, which are essential tools for studying stochastic models involving point processes. By developing these computational skills, readers gain the ability to analyze and understand a wide range of stochastic models, including Poisson-Cox, renewal, cluster, and branching (Kerstan-Hawkes) point processes.

The book's scope extends to examining classical and not-so-classical models in great detail, providing a comprehensive understanding of these models. Poisson-Cox, renewal, cluster, and branching (Kerstan-Hawkes) point processes are among the diverse topics covered, each chosen for their intrinsic interest and their ability to illustrate the theoretical principles discussed.

Written in a rigorous yet accessible style, this book caters to a diverse audience. It assumes a basic training in probability, making it suitable for earnest beginners seeking to delve into the world of point processes. However, it also appeals to upper-level graduate students and experienced researchers who are interested in advancing their knowledge in this field.

Throughout the text, real-world examples and applications are employed to demonstrate the practical significance of point processes. Queueing, information theory, stochastic geometry, and signal analysis are just a few of the areas where point processes find widespread use, highlighting their versatility and importance in modern research.

By providing a comprehensive and up-to-date introduction to point processes, this book serves as a valuable resource for students, researchers, and practitioners in the fields of probability, statistics, and applied mathematics. Its rigorous yet accessible approach makes it an essential tool for anyone seeking to deepen their understanding of this fascinating area of study.

Weight: 866g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030627553
Edition number: 1st ed. 2020