Ebook: Point Process Theory and Applications: Marked Point and Piecewise Deterministic Processes

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.

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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.

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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.

Content:
Front Matter....Pages i-xi
Front Matter....Pages 1-1
Introduction....Pages 3-7
Simple and Marked Point Processes....Pages 9-15
Construction of SPPs and MPPs....Pages 17-31
Compensators and Martingales....Pages 33-102
Likelihood Processes....Pages 103-118
Independence....Pages 119-141
Piecewise Deterministic Markov Processes....Pages 143-211
Front Matter....Pages 213-215
The Basic Models from Survival Analysis....Pages 217-229
Branching, Ruin, Soccer....Pages 231-246
A Model from Finance....Pages 247-276
Examples of Queueing Models....Pages 277-293
Front Matter....Pages 295-295
Differentiation of Cadlag Functions....Pages 297-299
Filtrations, Processes, Martingales....Pages 301-308
Back Matter....Pages 309-328

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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.

Content:
Front Matter....Pages i-xi
Front Matter....Pages 1-1
Introduction....Pages 3-7
Simple and Marked Point Processes....Pages 9-15
Construction of SPPs and MPPs....Pages 17-31
Compensators and Martingales....Pages 33-102
Likelihood Processes....Pages 103-118
Independence....Pages 119-141
Piecewise Deterministic Markov Processes....Pages 143-211
Front Matter....Pages 213-215
The Basic Models from Survival Analysis....Pages 217-229
Branching, Ruin, Soccer....Pages 231-246
A Model from Finance....Pages 247-276
Examples of Queueing Models....Pages 277-293
Front Matter....Pages 295-295
Differentiation of Cadlag Functions....Pages 297-299
Filtrations, Processes, Martingales....Pages 301-308
Back Matter....Pages 309-328
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