Skip to main content
SpringerLink
Log in
Birkhäuser
Book cover

Point Process Theory and Applications

Marked Point and Piecewise Deterministic Processes

  • Textbook
  • © 2006

Overview

Authors:
  1. Martin Jacobsen

    1. Department of Applied Mathematics and Statistics, University of Copenhagen Institute of Mathematical Sciences, Copenhagen Ø, Denmark

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • 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

Part of the book series: Probability and Its Applications (PA)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 69.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book USD 89.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (13 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  3. Applications

    1. Front Matter

      Pages 213-215
      Download chapter PDF

    2. The Basic Models from Survival Analysis

      Pages 217-229

    3. Branching, Ruin, Soccer

      Pages 231-246

    4. A Model from Finance

      Pages 247-276

    5. Examples of Queueing Models

      Pages 277-293

  4. Appendices

    1. Front Matter

      Pages 295-295
      Download chapter PDF

    2. Differentiation of Cadlag Functions

      Pages 297-299

    3. Filtrations, Processes, Martingales

      Pages 301-308

  5. Back Matter

    Pages 309-328
    Download chapter PDF
Back to top

Keywords

About this book

The book aims at presenting a detailed and mathematically rigorous exposition of the theory and applications of a class of point processes and piecewise deterministic p- cesses. The framework is suf?ciently general to unify the treatment of several classes of stochastic phenomena: point processes, Markov chains and other Markov processes in continuous time, semi-Markov processes, queueing and storage models, and li- lihood processes. There are applications to ?nance, insurance and risk, population models, survival analysis, and congestion models. A major aim has been to show the versatility of piecewise deterministic Markov processes for applications and to show how they may also become useful in areas where thus far they have not been much in evidence. Originally the plan was to develop a graduate text on marked point processes - dexed by time which would focus on probabilistic structure and be essentially se- contained. However, it soon became apparent that the discussion should naturally include a traditional class of continuous time stochastic processes constructed from certain marked point processes. This class consists of ‘piecewise deterministic p- cesses’; that is, processes with ?nitely many jumps on ?nite time intervals which, roughly speaking, develop deterministically between the random jump times. The - position starts with the point process theory and then uses this to treat the piecewise deterministic processes.

Reviews

From the reviews:

"The most remarkable aspect of the book is the reader-friendly structure and the style in which it has been written. The importance of the book both from the practical and from the theoretical standpoint is unquestionable. This book will be an essential part of every mathematical library."   —ZENTRALBLATT Math

"This book consists of three parts: (I) Theory, (II) Applications and (III) Appendices, that concisely summarize necessary mathematical concepts which are often found scattered among numerous texts. … The most remarkable aspect of the book is its reader-friendly structure and the style in which it has been written. The importance of this book, both from the practical and from the theoretical standpoint, is unquestionable. It will be an essential part of every mathematical library." (V. K. Oganyan, Mathematical Reviews, Issue 2007 a)

"This book deals with marked point processes on the positive real axis. It is rigorously written and largely self-contained. … Each chapter starts with an appealing introduction, including hints to the most important references. The reader is guided by clearly stated comments and hints. … Many examples and exercises are given … . This book is suitable for advanced graduate and postgraduate students in mathematics with some preknowledge in this area. It will also be valuable for preparing a respective lecture course." (Martin Schlather, Journal of the American Statistical Association, Vol. 102 (479), 2007)

"The book will serve as a guide to the comprehensive study of the subject, and—more likely—as a reference book, inevitably a standard one. … Martin Jacobsen write an accessible book is a true gift to the mathematics community. … This is a good book, and an important one. … Every researcher with even a passing interest in the subject will want this book on his or her shelf." (Philip Protter, SIAM Review, Vol. 49 (1), 2007)

Authors and Affiliations

  • Department of Applied Mathematics and Statistics, University of Copenhagen Institute of Mathematical Sciences, Copenhagen Ø, Denmark

    Martin Jacobsen

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation