Measure Theory and Filtering Introduction and Applications [Paperback]

This book is a resource for non-statisticians implementing filtering methods, which covers applications in finance, genetics and population.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.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.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 finanl£S