Response Theory for Point Processes

Fluctuations, Feedback, and Causal Event Systems
1. Auflage 2027
ISBN: 978-1-041-54944-4
Verlag: Taylor & Francis

Buch, Englisch, 194 Seiten, Format (B × H): 156 mm x 234 mm

Response Theory for Point Processes develops a systematic response-theoretic calculus for temporal point processes. Point-process theory is usually organised around laws, intensities, moment measures, covariance measures, cumulants, and spectra. These objects describe how event streams fluctuate.

This book asks the complementary question: how does an event-generating mechanism respond when it is perturbed, observed, or placed in feedback? The central distinction is between fluctuation and response. Cumulants, covariance measures, Bartlett spectra, and polyspectra describe spontaneous variation under a fixed law, whereas response kernels, closed-loop resolvents, and feedback kernels describe directed input-output propagation. The linear Hawkes process provides a canonical worked example, allowing its excitation kernel, branching cascade, resolvent, and Bartlett spectrum to be compared explicitly. Nonlinear feedback then shows how higher-order fluctuation structure can enter lower-order summaries through cumulant order mixing.

The emphasis throughout is structural: separating event fluctuation, causal response, observation effects, feedback dressing, nonlinear order mixing, and adaptive sensing within a common mathematical framework. The book is intended as a specialist research monograph for applied probabilists, statisticians, stochastic-systems researchers, and signal-processing researchers working with event-stream data.

Zielgruppe

Postgraduate, Professional Reference, and Undergraduate Advanced

Autoren/Hrsg.

Clark, Daniel E.

Fachgebiete

• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Signalverarbeitung
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Signalverarbeitung, Bildverarbeitung, Scanning

Inhaltsverzeichnis

1 Introduction 2 Fluctuation and Response 3 Response Kernels for Temporal Point Processes 4 Hawkes Processes and Causal Resolvents 5 Feedback Closure and Linear Dressing 6 Renewal, Queueing, and Classical Event Response 7 Cumulant Scattering and Nonlinear Feedback 8 Spectral Representation and Polyspectra 9 Observation, Identification, and Design 10 Adaptive Sensing and Dual Control of Event Streams 11 Perturbative and Non-Perturbative Structure 12 Diagrammatic Expansions for Point-Process Response

Über Autor(innen)

Daniel E. Clark is Chair in Electronics and Computer Science at the University of Southampton, UK. His research lies at the interface of applied probability, point-process theory, stochastic systems, and statistical inference, with particular emphasis on random measures and fields, point-process information, response theory, inverse problems, and functional methods for event-based models.