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  3. Measure Theory and Filtering
  • Cited by 39
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    • Publisher:
      Cambridge University Press
      Publication date:
      July 2010
      September 2004
      ISBN:
      9780511755330
      9780521838030
      9781107410718
      DOI:
      https://doi.org/10.1017/CBO9780511755330
      Dimensions:
      (253 x 177 mm)
      Weight & Pages:
      0.604kg, 270 Pages
      Dimensions:
      (244 x 170 mm)
      Weight & Pages:
      0.44kg, 270 Pages
      • 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)
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    • Selected: Digital
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    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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