Overview
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.
Full Product Details
Author: Damir Z. Arov ,
Harry Dym
Publisher: Springer Nature Switzerland AG
Imprint: Springer Nature Switzerland AG
Edition: Softcover reprint of the original 1st ed. 2018
Volume: 266
Dimensions:
Width: 15.50cm
, Height: 2.20cm
, Length: 23.50cm
Weight: 0.640kg
ISBN: 9783030099442
ISBN 10: 303009944
Pages: 405
Publication Date: 25 December 2018
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: Manufactured on demand
We will order this item for you from a manufactured on demand supplier.
Reviews
“The book is a product of more than 20 years of collaborations between the two mathematicians belonging to Ukrainian and Isreali schools of functional analysis. They succeeded in writing a book on technically complicated subject that is easy to read. The book is strongly recommended to all researchers and graduate students in theoretical and applied probability and functional analysis … .” (Anatoliy Malarenko, Mathematical Reviews, February, 2019)
The book is a product of more than 20 years of collaborations between the two mathematicians belonging to Ukrainian and Isreali schools of functional analysis. They succeeded in writing a book on technically complicated subject that is easy to read. The book is strongly recommended to all researchers and graduate students in theoretical and applied probability and functional analysis ... . (Anatoliy Malarenko, Mathematical Reviews, February, 2019)
