TY  - BOOK
AU  - Jacobsen,Martin
ED  - SpringerLink (Online service)
TI  - Point Process Theory and Applications: Marked Point and Piecewise Deterministic Processes 
T2  - Probability and its Applications
SN  - 9780817644635
U1  - 519.2 23
PY  - 2006///
CY  - Boston, MA
PB  - Birkhäuser Boston
KW  - MATHEMATICS
KW  - FINANCE
KW  - MATHEMATICAL OPTIMIZATION
KW  - DISTRIBUTION (PROBABILITY THEORY)
KW  - ECONOMICS
KW  - STATISTICS
KW  - PROBABILITY THEORY AND STOCHASTIC PROCESSES
KW  - APPLICATIONS OF MATHEMATICS
KW  - STATISTICS FOR BUSINESS/ECONOMICS/MATHEMATICAL FINANCE/INSURANCE
KW  - MEASURE AND INTEGRATION
KW  - OPTIMIZATION
KW  - QUANTITATIVE FINANCE
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/0-8176-4463-6
ER  -