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.
Product Identifiers
Publisher
Cambridge University Press
ISBN-13
9781107410718
eBay Product ID (ePID)
117553933
Product Key Features
Author
Lakhdar Aggoun, Robert J. Elliott
Publication Name
Measure Theory and Filtering: Introduction and Applications
Format
Paperback
Language
English
Subject
Engineering & Technology, Mathematics
Publication Year
2012
Type
Textbook
Number of Pages
270 Pages
Dimensions
Item Height
244mm
Item Width
170mm
Item Weight
440g
Additional Product Features
Title_Author
Lakhdar Aggoun, Robert J. Elliott
Series Title
Cambridge Series in Statistical and Probabilistic Mathematics