Description
Measure Theory and Filtering
Introduction and Applications
Cambridge Series in Statistical and Probabilistic Mathematics Series
Authors: Aggoun Lakhdar, Elliott Robert J.
This book is a resource for non-statisticians implementing filtering methods, which covers applications in finance, genetics and population.
Language: EnglishSubject for Measure Theory and Filtering:
61.17 €
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Add to cart the print on demand of Aggoun Lakhdar, Elliott Robert J.
Measure Theory and Filtering
Publication date: 10-2012
Support: Print on demand
Publication date: 10-2012
Support: Print on demand
96.92 €
Subject to availability at the publisher.
Add to cart the book of Aggoun Lakhdar, Elliott Robert J.
Measure theory and filtering: Introduction with applications
Publication date: 09-2004
270 p. · 18.4x26.2 cm · Hardback
Publication date: 09-2004
270 p. · 18.4x26.2 cm · Hardback
Description
/li>Contents
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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.
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.
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