This book deals with the relation between the past and the future of a real, one-dimensional, stationary Gaussian process. Kolmogorov and Wiener showed how best to predict the future knowing the whole past. The more difficult problem, when only a finite segment of the past is known, was solved by M. G. Krein. A full treatment of this problem, and theprerequisites for dealing with it, occupies most of the book. The first three chapters are devoted to the necessary background in function theory, Hardy spaces and probability. Later chapters introduce the spectral theory of a weighted string developed by Krein and certain Hilbert spaces of entire functions introduced by L. de Branges. Various other connections between past and future are considered, such as mixing and Markovian character. The final chapter treats the problem of interpolation, when the whole process is known except for a gap and it is desired to predict what happens there.
Sub Title | No |
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Author | H.Dym & H.P. Mckean |
About Author | H.Dym is Professor of Mathematics at the Weizmann Institute of Science Rehovot, Israel, and H.P. Mckean is Professor of Mathematics at New York University's Courant Institute. Their text is geared primrily toward students of mathematics, but electrical engineers and others dealing with the practical aspects of predictio will aslo find it of interest. Numerous exercises appear throughout the text, many with hints for their solution. |
Content |
No |
ISBN 10 Digit | 048646279X |
ISBN 13 Digit | 9780486462790 |
Pages | 333 |
Binding | Paperback |
Year of Publication | 2008 |
Edition of Book | 1 |
Language | English |
Illustrations | No |
About Book | Yes |
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