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Other titles in the Cambridge Series in Statistical and Probabilistic Mathematic series:
Measure Theory and Filtering: Introduction with Applications (Cambridge Series on Statistical and Probabilistic Mathematic)by Lakhdar Aggoun
Synopses & Reviews
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.
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.
Aimed primarily at those outside of the field of statistics, this book not only provides an accessible introduction to measure theory, stochastic calculus, and stochastic processes, with particular emphasis on martingales and Brownian motion, but develops into an excellent user's guide to filtering. Including exercises for students, it will be a complete resource for engineers, signal processing researchers, or anyone with an interest in practical implementation of filtering techniques, in particular, the Kalman filter. Three separate chapters concentrate on applications arising in finance, genetics, and population modelling.
A resource for non-statisticians implementing filtering methods. Covers applications in finance and genetics.
About the Author
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.
Table of Contents
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.
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