Measure Theory and Filtering

ISBN-13: 9780521838030 / Angielski / Twarda / 2004 / 270 str.

Lakhdar Aggoun; Robert Elliott; Robert J. Elliott

Opis

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.

Recenzje

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.' Journal of Applied Statistics

Spis treści

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.