Point Process Theory and Applications: Marked Point and Piecewise Deterministic Processes (Probability and Its Applications (duplicate)) - Hardcover

Jacobsen, Martin

Hardcover

ISBN 10: 0817642153 ISBN 13: 9780817642150

Publisher: Birkhäuser, 2005

Synopsis

Mathematically rigorous exposition of the basic theory of marked point processes and piecewise deterministic stochastic processes

Point processes are constructed from scratch with detailed proofs

Includes applications with examples and exercises in survival analysis, branching processes, ruin probabilities, sports (soccer), finance and risk management, and queueing theory

Accessible to a wider cross-disciplinary audience

About this title

From the Back Cover

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 focus is on point processes that generate only finitely many points in finite time intervals, resulting in piecewise deterministic processes with "few jumps". The point processes are constructed from scratch with detailed proofs and their distributions characterized using compensating measures and martingale structures. Piecewise deterministic processes are defined and identified with certain marked point processes, which are then used in particular to construct and study a large class of piecewise deterministic Markov processes, whether time homogeneous or not.

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 in survival analysis, branching processes, ruin probabilities, sports (soccer), finance and risk management (arbitrage and portfolio trading strategies), and queueing theory.

Graduate students and researchers interested in probabilistic modeling and its applications 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, an explanatory introduction to each chapter highlights those portions that are crucial and those that can be omitted by non-specialists, making the material more accessible to a wider cross-disciplinary audience.

Edition details

• Publisher: Birkhäuser
• Publication date: 2005
• Language: English
• ISBN 10: 0817642153
• ISBN 13: 9780817642150
• Binding: Hardcover
• Number of pages: 328