Hilbert and Banach Space-Valued Stochastic Processes

CONTENTS
Preface
I. Introduction and preliminaries
	1.1. Stationary processes
	1.2. Harmonizable processes
	1.3. Multidimensional and other extensions
	Bibliographical notes
II. Hilbert modules and covariance kernels
	2.1. Normal Hilbert B(H)-modules
	2.2. Submodules, operators and functionals
	2.3. Characterization and structure
	2.4. Positive definite kernels and reproducing kernel spaces
	2.5. Harmonic analysis for normal Hilbert B(H)-modules
	Bibliographical notes
III. Stochastic measures and operator-valued bimeasures
	3.1. Semivariations and variations
	3.2. Orthogonally scattered dilations
	3.3. Gramian orthogonally scattered dilations
	3.4. The spaces L1(F) and L2(F)
	3.5. L2-spaces for bimeasures
	3.6. Riesz type theorems
	3.7. Weak topology on measures
	3.8. A Chouquet type theorem
	Bibliographical notes
IV. Radon-Nikodým derivatives and Schauder basic measures
	4.1. Pseudo Radon-Nikodým derivatives (1)
	4.2. Pseudo Radon-Nikodým derivatives (2)
	4.3. Schauder basic measures
	4.4. Gramian Schauder basic measures
	Bibliographical notes
V. Multidimensional stochastic processes
	5.1. General concepts
	5.2. Stationary processes
	5.3. Harmonizable processes
	5.4. V-bounded processes
	5.5. Cramér and Karhunen classes
	5.6. Operator representations
	5.7. Series representations
	5.8. Moving average representations
	5.10. Subordination
	Bibliographical notes
VI. Special topics
	6.1. Wold decompositions
	6.2. Cramér decompositions
	6.3. The KF-class
	6.4. Gramian uniformly bounded linearly stationary processes
	6.5. Periodically correlated processes
	6.6. Absolutely summing processes
	6.7. Final remarks
	Bibliographical notes
VII. Applications
	7.1. Prediction problems
	7.2. Kalman filter
	7.3. Sampling theorems
	7.4. Strong laws of large numbers
	Bibliographical notes
VIII. Generalizations
	8.1. Banach space-valued random variables
	8.2. The spaces B(U, H) and B(U, U*)
	8.3. B(U, H)-valued measures
	8.4. B(U, U*)-valued measures and bimeasures
	8.5. B(U, H)-valued processes
	8.6. B(U, V)-valued measures
	8.7. B(U, V)-valued processes
	Bibliographical notes
References
Indices
	Notation Index
	Author Index
	Subject Index