Overview
- 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
Part of the book series: Probability Theory and Stochastic Modelling (PTSM, volume 98)
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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 Poisson–Cox, renewal, cluster and branching (Kerstan–Hawkes) 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.
Authors and Affiliations
About the author
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.
Bibliographic Information
Book Title: Point Process Calculus in Time and Space
Book Subtitle: An Introduction with Applications
Authors: Pierre Brémaud
Series Title: Probability Theory and Stochastic Modelling
DOI: https://doi.org/10.1007/978-3-030-62753-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-62752-2Published: 06 December 2020
Softcover ISBN: 978-3-030-62755-3Published: 07 December 2021
eBook ISBN: 978-3-030-62753-9Published: 05 December 2020
Series ISSN: 2199-3130
Series E-ISSN: 2199-3149
Edition Number: 1
Number of Pages: XIII, 556
Number of Illustrations: 8 b/w illustrations
Topics: Probability Theory and Stochastic Processes, Fourier Analysis