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E-raamat: Random And Vector Measures

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(Univ Of California, Riverside, Usa)
  • Formaat: 552 pages
  • Sari: Series On Multivariate Analysis 9
  • Ilmumisaeg: 31-Aug-2011
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789814458726
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Random And Vector MeasuresSuurem pilt
  • Formaat: 552 pages
  • Sari: Series On Multivariate Analysis 9
  • Ilmumisaeg: 31-Aug-2011
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789814458726
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The book is devoted to the structural analysis of vector and random (or both) valued countably additive measures, and used for integral representations of random fields. The spaces can be Banach or Frechet types. Special attention is given to Bochner's boundedness principle and Grothendieck's representation unifying and simplyfying stochastic integrations. Several stationary aspects, extensions and random currents as well as related multilinear forms are analyzed, whilst numerous new procedures and results are included, and many research areas are opened up which also display the geometric aspects in multi dimensions.
Preface vii
1 Introduction and Motivation
1(22)
1.1 Introducing Vector Valued Measures
1(2)
1.2 Basic Structures
3(7)
1.3 Additivity Properties of Vector Valued Measures
10(8)
1.4 Complements and Exercises
18(5)
Bibliographical Notes
21(2)
2 Second Order Random Measures and Representations
23(38)
2.1 Introduction
23(2)
2.2 Structures of Second Order Random Measures
25(13)
2.3 Shift Invariant Second Order Random Measures
38(11)
2.4 A Specialization of Random Measures Invariant on Subgroups
49(5)
2.5 Complements and Exercises
54(7)
Bibliographical Notes
58(3)
3 Random Measures Admitting Controls
61(64)
3.1 Structural Analysis
62(12)
3.2 Controls for Weakly Stable Random Measures
74(9)
3.3 Integral Representations of Stable Classes by Random Measures
83(11)
3.4 Integral Representations of Some Second Order Processes
94(19)
3.5 Complements and Exercises
113(12)
Bibliographical Notes
122(3)
4 Random Measures in Hilbert Space: Specialized Analysis
125(42)
4.1 Bilinear Functional Associated with Random Measures
126(7)
4.2 Local Classes of Random Fields and Related Measures
133(7)
4.3 Bilinear Forms and Random Measures
140(10)
4.4 Random Measures with Constraints
150(7)
4.5 Complements and Exercises
157(10)
Bibliographical Notes
164(3)
5 More on Random Measures and Integrals
167(50)
5.1 Random Measures, Bimeasures and Convolutions
167(10)
5.2 Bilinear Forms and Random Measure Algebras
177(12)
5.3 Vector Integrands and Integrals with Stable Random Measures
189(12)
5.4 Positive and Other Special Classes of Random Measures
201(6)
5.5 Complements and Exercises
207(10)
Bibliographical Notes
215(2)
6 Martingale Type Measures and Their Integrals
217(52)
6.1 Random Measures and Deterministic Integrands
218(3)
6.2 Random Measures and Stochastic Integrands
221(15)
6.3 Random Measures, Stopping Times and Stochastic Integration
236(14)
6.4 Generalizations of Martingale Integrals
250(11)
6.5 Complements and Exercises
261(8)
Bibliographical Notes
267(2)
7 Multiple Random Measures and Integrals
269(104)
7.1 Basic Quasimartingale Spaces and Integrals
270(18)
7.2 Multiple Random Measures, Part I: Cartesian Products
288(15)
7.3 Multiple Random Measures, Part II: Noncartesian Products
303(14)
7.4 Random Line Integrals With Fubini and Green-Stokes Theorems
317(18)
7.5 Random Measures on Partially Ordered Sets
335(15)
7.6 Multiple Random Integrals Using White Noise Methods
350(12)
7.7 Complements and Exercises
362(11)
Bibliographical Notes
369(4)
8 Vector Measures and Integrals
373(74)
8.1 Vector Measures of Nonfhiitc Variation
373(5)
8.2 Vector Integration with Measures of Finite Semivariation, Part I
378(8)
8.3 Vector Integration with Measures of Finite Semivariation, Part II
386(17)
8.4 Some Applications of Vector Measure Integration, Part I
403(17)
8.5 Some Applications of Vector Measure Integration, Part II
420(16)
8.6 Complements and Exercises
436(11)
Bibliographical Notes
443(4)
9 Random and Vector Multimeasures
447(50)
9.1 Bimeasures and Multiple Integrals
447(10)
9.2 Bimeasure Domination, Dilations and Representations of Processes
457(11)
9.3 Spectral Analysis of Second Order Fields and Bimeasures
468(10)
9.4 Multimeasures and Multilinear Forms
478(11)
9.5 Complements and Exercises
489(8)
Bibliographical Notes
494(3)
Bibliography 497(26)
Notation Index 523(6)
Author Index 529(6)
Subject Index 535
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