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Matériel obligatoire et recommandé
Point Processes Theory and Applications
Jacobsen, Martin
Éditeur : BIRKHAUSSER
ISBN papier: 9780817642150
Parution : 2006
Code produit : 1135500
Catégorisation :
Livres /
Science /
Mathématique /
Mathématiques
Formats disponibles
| Format | Qté. disp. | Prix* | Commander |
|---|---|---|---|
| Livre papier | En rupture de stock** |
Prix membre : 35,39 $ Prix non-membre : 39,32 $ |
*Les prix sont en dollars canadien. Taxes et frais de livraison en sus.
**Ce produits est en rupture de stock mais sera expédié dès qu'ils sera disponible.
Description
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 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, finance and risk management (arbitrage and portfolio trading strategies), queueing theory, and sports (soccer).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.