Point Process Calculus in Time and Space
An Introduction with Applications
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Beschreibung
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 alsointerest upper graduate students and experienced researchers.
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.
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
Autor*in
Pierre Brémaud
Themen in »Point Process Calculus in Time and Space«
60xx, 90xx, 93xx, 94xx point process random measure Poisson process renewal theory stochastic calculus signal analysis martingales Queueing Theory Palm Probability Information and Communication, Circuits Stochastic Systems and Control Information theory mathematical programming