Point Process Theory and Applications

Marked Point and Piecewise Deterministic Processes

  • Martin Jacobsen

Part of the Probability and its Applications book series (PA)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Theory

  3. Applications

    1. Front Matter
      Pages 213-215
    2. Pages 231-246
    3. Pages 247-276
  4. Appendices

    1. Front Matter
      Pages 295-295
  5. Back Matter
    Pages 309-328

About this book

Introduction

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.

Keywords

Analysis Branching process Excel Markov process Martingale Measure Probability theory Stochastic Processes Survival analysis filtration modeling point process queueing theory stochastic process

Authors and affiliations

  • Martin Jacobsen
    • 1
  1. 1.Department of Applied Mathematics and StatisticsUniversity of Copenhagen Institute of Mathematical SciencesCopenhagen ØDenmark

Bibliographic information

  • DOI https://doi.org/10.1007/0-8176-4463-6
  • Copyright Information Birkhäuser Boston 2006
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4215-0
  • Online ISBN 978-0-8176-4463-5
  • About this book