Measure Theory and Filtering by Lakhdar Aggoun, Robert J. Ell... - 9781107410718

Measure Theory and FilteringIntroduction and Applications\nAuthor(s): Lakhdar Aggoun, Robert J. Elliott\nFormat: Paperback\nPublisher: Cambridge University Press, United Kingdom\nImprint: Cambridge University Press\nISBN-13: 9781107410718, 978-1107410718\nSynopsis\nThe 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 Kal.