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040			_aNISER LIBRARY _cNISER LIBRARY _beng
082	0	0	_a519.218.7 _bDYM-G
100	1		_aDym, H.
245	1	0	_aGaussian processes, function theory, and the inverse spectral problem
260			_aMineola, N.Y. : _bDover Publications, _c2008.
300			_axiii, 333 p. : _bill. ; _c22 cm.
490			_aDover books on mathematics
500			_a"This Dover edition, first published in 2008, is an unabridged republication of the work originally published in the "Probability and Mathematical Statistics" series by Academic Press, Inc., New York, in 1976."
504			_aIncludes bibliographical references (p. 323-328) and index.
520			_aThis 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.
650		0	_aGaussian processes.
650		0	_aStationary processes.
650		0	_aSpectral theory (Mathematics)
650		0	_aPrediction theory.
700	1		_aMcKean, H. P.
856	4	2	_3Reviews _uhttps://www.goodreads.com/book/show/3113648-gaussian-processes-function-theory-and-the-inverse-spectral-problem#CommunityReviews
942			_2udc _cBK
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