Jacobsen Point Process Theory and Applications

Marked Point and Piecewise Deterministic Processes
1. Auflage 2006
ISBN: 978-0-8176-4463-5
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 324 Seiten, Web PDF

Reihe: Mathematics and Statistics (R0)

This text offers a mathematically rigorous exposition of the basic theory of marked point processes developing randomly over time, and shows how this theory may be used to treat piecewise deterministic stochastic processes in continuous time. The point processes are constructed from scratch with detailed proofs. The second part of the book addresses applications of the just developed theory; this analysis of various models in applied statistics and probability includes examples and exercises. Graduate students and researchers will find this text an excellent resource, requiring for mastery a solid foundation in probability theory, measure and integration, as well as some knowledge of stochastic processes and martingales. However, the material is presented so as to be accessible to a wider cross-disciplinary audience.

Zielgruppe

Research

Autoren/Hrsg.

Jacobsen, Martin

Inhaltsverzeichnis

Theory.- Simple and Marked Point Processes.- Construction of SPPs and MPPs.- Compensators and Martingales.- Likelihood Processes.- Independence.- Piecewise Deterministic Markov Processes.- Applications.- The Basic Models from Survival Analysis.- Branching, Ruin, Soccer.- A Model from Finance.- Examples of Queueing Models.- Appendices.- Differentiation of Cadlag Functions.- Filtrations, Processes, Martingales.