Measure Theory and Filtering

Erscheinungsjahr 2015
ISBN: 978-0-521-83803-0
Verlag: Cambridge University Press

Buch, Englisch, Band 15, 268 Seiten, Format (B × H): 175 mm x 250 mm, Gewicht: 650 g

Reihe: Cambridge Series in Statistical and Probabilistic Mathematics

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.

Autoren/Hrsg.

Aggoun, Lakhdar

Elliott, Robert J.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

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.

Über Autor(innen)

Elliott, Robert J.
Robert Elliott is the RBC Financial Group Professor of Finance at the University of Calgary, Canada.

Aggoun, Lakhdar
Lakhdar Aggoun is an Associate Professor in the Department of Mathematics and Statistics at Sultan Qabos University, Oman.