An Introduction to the Theory of Point Processes

An Introduction to the Theory of Point Processes

1998 | D. J. Daley D. Vere-Jones
This book, "An Introduction to the Theory of Point Processes," is a comprehensive and detailed exploration of the theory of point processes, authored by D. J. Daley and D. Vere-Jones. It is part of the Springer Series in Statistics and is intended for graduate students and researchers in applied fields. The book covers a wide range of topics, from historical background to advanced theoretical concepts, with a focus on both rigorous mathematical treatment and practical applications. The authors adopt a historical approach, starting with foundational concepts and gradually delving into more abstract and general theories. Key topics include Poisson processes, renewal processes, finite point processes, random measures, cluster processes, infinitely divisible processes, and doubly stochastic processes. The book also discusses convergence concepts, limit theorems, stationary point processes, spectral theory, Palm theory, conditional intensities, likelihoods, and exterior conditioning. The book includes appendices that provide essential background in topology, measure theory, and martingale theory, making it accessible to a broad audience. The authors acknowledge the contributions of numerous colleagues and institutions, and they express gratitude to their families for their support throughout the writing process.This book, "An Introduction to the Theory of Point Processes," is a comprehensive and detailed exploration of the theory of point processes, authored by D. J. Daley and D. Vere-Jones. It is part of the Springer Series in Statistics and is intended for graduate students and researchers in applied fields. The book covers a wide range of topics, from historical background to advanced theoretical concepts, with a focus on both rigorous mathematical treatment and practical applications. The authors adopt a historical approach, starting with foundational concepts and gradually delving into more abstract and general theories. Key topics include Poisson processes, renewal processes, finite point processes, random measures, cluster processes, infinitely divisible processes, and doubly stochastic processes. The book also discusses convergence concepts, limit theorems, stationary point processes, spectral theory, Palm theory, conditional intensities, likelihoods, and exterior conditioning. The book includes appendices that provide essential background in topology, measure theory, and martingale theory, making it accessible to a broad audience. The authors acknowledge the contributions of numerous colleagues and institutions, and they express gratitude to their families for their support throughout the writing process.
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