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  3. Measure Theory and Filtering
  • Cited by 39
Publisher:
Cambridge University Press
Online publication date:
July 2010
Print publication year:
2004
Online ISBN:
9780511755330
DOI:
https://doi.org/10.1017/CBO9780511755330
Subjects:
Mathematics, Abstract Analysis, General Statistics and Probability, Applied Probability and Stochastic Networks, Statistics and Probability
Series:
Cambridge Series in Statistical and Probabilistic Mathematics (15)
Information

Book description

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.

Reviews

Review of the hardback:'… useful to those students and scientists in signal processing, mathematical finance and genetics, wishing to incorporate measure-theoretic probability techniques into their predictions. It is also an excellent user's guide to filtering with interesting applications arising in difference arenas.'

Source: Journal of Applied Statistics

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