Measure Theory and Filtering
Introduction and Applications
Seiten
2004
Cambridge University Press (Verlag)
978-0-521-83803-0 (ISBN)
Cambridge University Press (Verlag)
978-0-521-83803-0 (ISBN)
This book provides an accessible introduction to measure theory and stochastic calculus, and develops into an excellent users' guide to filtering. A complete resource for engineers, or anyone with an interest in implementation of filtering techniques. Three chapters concentrate on applications from finance, genetics and population modelling. Also includes exercises.
The estimation of noisily observed states from a sequence of data has traditionally incorporated ideas from Hilbert spaces and calculus-based probability theory. As conditional expectation is the key concept, the correct setting for filtering theory is that of a probability space. Graduate engineers, mathematicians and those working in quantitative finance wishing to use filtering techniques will find in the first half of this book an accessible introduction to measure theory, stochastic calculus, and stochastic processes, with particular emphasis on martingales and Brownian motion. Exercises are included. The book then provides an excellent users' guide to filtering: basic theory is followed by a thorough treatment of Kalman filtering, including recent results which extend the Kalman filter to provide parameter estimates. These ideas are then applied to problems arising in finance, genetics and population modelling in three separate chapters, making this a comprehensive resource for both practitioners and researchers.
The estimation of noisily observed states from a sequence of data has traditionally incorporated ideas from Hilbert spaces and calculus-based probability theory. As conditional expectation is the key concept, the correct setting for filtering theory is that of a probability space. Graduate engineers, mathematicians and those working in quantitative finance wishing to use filtering techniques will find in the first half of this book an accessible introduction to measure theory, stochastic calculus, and stochastic processes, with particular emphasis on martingales and Brownian motion. Exercises are included. The book then provides an excellent users' guide to filtering: basic theory is followed by a thorough treatment of Kalman filtering, including recent results which extend the Kalman filter to provide parameter estimates. These ideas are then applied to problems arising in finance, genetics and population modelling in three separate chapters, making this a comprehensive resource for both practitioners and researchers.
Lakhdar Aggoun is an Associate Professor in the Department of Mathematics and Statistics at Sultan Qabos University, Oman. Robert Elliott is the RBC Financial Group Professor of Finance at the University of Calgary, Canada.
Part I. Theory: 1. Basic probability concepts; 2. Stochastic processes; 3. Stochastic calculus; 4. Change of measures; Part II. Applications: 5. Kalman filtering; 6. Financial applications; 7. A genetics model; 8. Hidden populations.
| Erscheint lt. Verlag | 13.9.2004 |
|---|---|
| Reihe/Serie | Cambridge Series in Statistical and Probabilistic Mathematics |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 184 x 262 mm |
| Gewicht | 604 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Statistik | |
| Technik ► Nachrichtentechnik | |
| ISBN-10 | 0-521-83803-7 / 0521838037 |
| ISBN-13 | 978-0-521-83803-0 / 9780521838030 |
| Zustand | Neuware |
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