Hilbert And Banach Space-valued Stochastic Processes
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A01=Yuichiro Kakihara
Author_Yuichiro Kakihara
Category=PBT
Category=PBWL
CramAfA(C)r and Karhunen Classes
Cramér and Karhunen Classes
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Harmonizable Processes
Infinite Dimensional Stochastic Processes
Kalman Filter
Normal Hilbert Modules
Periodically Correlated Processes
Representing Measures
Reproducing Kernels
Sampling Theorems
Scalar and Operator Bimeasures
Series Representations
Stationary Dilation
Stationary Processes
Strong Laws of Large Numbers
Uniformly Bounded Linearly Stationary Processes
V-bounded Processes
Wold and CramAfA(C)r Decompositions
Wold and Cramér Decompositions
Product details
- ISBN 9789811211744
- Publication Date: 11 Aug 2021
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
