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Gaussian Processes, Function Theory, and the Inverse Spectral Problem
Harry DymHenry P. McKean
出版Courier Corporation, 2008-01-01
主題Mathematics / Set TheoryMathematics / Probability & Statistics / General
ISBN048646279X9780486462790
URLhttp://books.google.com.hk/books?id=xM3PStPHY-sC&hl=&source=gbs_api
EBookSAMPLE
註釋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 the prerequisites 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.