Damir Z. Arov; Harry Dym Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems 9783030099442

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Автор: Damir Z. Arov; Harry Dym
Название: Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems
ISBN: 9783030099442
Издательство: Springer
Классификация:

Функциональный анализ и преобразования

Вероятность и статистика

Стохастика

ISBN-10: 303009944X
Обложка/Формат: Soft cover
Страницы: 405
Вес: 0.64 кг.
Дата издания: 2018
Серия: Operator Theory: Advances and Applications
Язык: English
Издание: Softcover reprint of
Иллюстрации: XIV, 405 p.
Размер: 234 x 156 x 22
Читательская аудитория: General (us: trade)
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: This monograph deals primarily with the prediction of vector valued stochastic processes that are either weakly stationary, or have weakly stationary increments, from finite segments of their past. The main focus is on the analytic counterpart of these problems, which amounts to computing projections onto subspaces of a Hilbert space of p x 1 vector valued functions with an inner product that is defined in terms of the p x p matrix valued spectral density of the process. The strategy is to identify these subspaces as vector valued de Branges spaces and then to express projections in terms of the reproducing kernels of these spaces and/or in terms of a generalized Fourier transform that is obtained from the solution of an associated inverse spectral problem. Subsequently, the projection of the past onto the future and the future onto the past is interpreted in terms of the range of appropriately defined Hankel operators and their adjoints, and, in the last chapter, assorted computations are carried out for rational spectral densities. The underlying mathematics needed to tackle this class of problems is developed in careful detail, but, to ease the reading, an attempt is made to avoid excessive generality. En route a number of results that, to the best of our knowledge, were only known for p = 1 are generalized to the case p > 1.
Дополнительное описание: Introduction.- Analytic preliminaries.- The de Branges spaces B(E) and H(A).- Three extension problems.- Spectral functions for ci problems.- Inverse spectral problems.- Generalizations.- Real and symmetric constraints.- Past and Future.- Conservative and

Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems, Damir Z. Arov; Harry Dym