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Hilbert and Banach space-valued stochastic processes

Hilbert and Banach space-valued stochastic processes
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Field name Details
Dewey Class 519.23
Title Hilbert and Banach space-valued stochastic processes (M) / Yûichirô Kakihara
Author Kakihara, Yūichirō
Publication Singapore : World Scientific , 2021
Physical Details xi, 526 pag. ; 24 cm.
Series Series on multivariate analysis ; 13
ISBN 9789811211744
Summary Note "This is a development of the book entitled Multidimensional Second Order Stochastic Processes. It provides a research expository treatment of infinite-dimensional stationary and nonstationary stochastic processes or time series, based on Hilbert and Banach space-valued second order random variables. Stochastic measures and scalar or operator bimeasures are fully discussed to develop integral representations of various classes of nonstationary processes such as harmonizable, V-bounded, Cramér and Karhunen classes as well as the stationary class. A new type of the Radon-Nikodým derivative of a Banach space-valued measure is introduced, together with Schauder basic measures, to study uniformly bounded linearly stationary processes. Emphasis is on the use of functional analysis and harmonic analysis as well as probability theory. Applications are made from the probabilistic and statistical points of view to prediction problems, Kalman filter, sampling theorems and strong laws of large numbers. Generalizations are made to consider Banach space-valued stochastic processes to include processes of pth order for p ≥ 1. Readers may find that the covariance kernel is always emphasized and reveals another aspect of stochastic processes. This book is intended not only for probabilists and statisticians, but also for functional analysts and communication engineers."--:
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0000000044413 519.216 KAK
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