Bharucha-Reid Probabilistic Analysis and Related Topics

Volume 2
1. Auflage 2014
ISBN: 978-1-4832-7553-6
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 220 Seiten, Web PDF

Probabilistic Analysis and Related Topics, Volume 2 focuses on the integrability, continuity, and differentiability of random functions, as well as functional analysis, measure theory, operator theory, and numerical analysis. The selection first offers information on the optimal control of stochastic systems and Gleason measures. Discussions focus on convergence of Gleason measures, random Gleason measures, orthogonally scattered Gleason measures, existence of optimal controls without feedback, random necessary conditions, and Gleason measures in tensor products. The text then elaborates on an introduction to nonstandard analysis and hyperfinite probability theory, including applications to stochastic processes, conversion from nonstandard to standard measure spaces, and an introduction to nonstandard analysis. The text examines stochastic matrices, ergodic Markov chains, and measures on semigroups, as well as limit theorems for convolution products of probability measures on completely simple semigroups; ergodicity of Markov chains and probability measures on semigroups; and limits of convolutions in groups and semigroups. The selection is a dependable source of data for mathematicians and researchers interested in the general theory of random functions.

Autoren/Hrsg.

Bharucha-Reid, A. T.

Inhaltsverzeichnis

1;Front Cover;1
2;Probabilistic Analysis and Related Topics;4
3;Copyright Page;5
4;Table of Contents;6
5;List of Contributors;8
6;Preface;10
7;Chapter 1. Optimal Control of Stochastic Systems;14
7.1;I. Introduction;15
7.2;II. Existence of Optimal Controls without Feedback;16
7.3;III. Existence of Optimal Feedback Controls;25
7.4;IV. Random Necessary Conditions;42
7.5;V. Analytic Necessary Conditions;49
7.6;ACKNOWLEDGMENTS;78
7.7;REFERENCES;78
8;Chapter 2. Gleason Measures;82
8.1;I. Introduction;82
8.2;II. Generalities;84
8.3;III. Orthogonally Scattered Gleason Measures;88
8.4;IV. L2§(H) -Spaces and Isometries Generated by OSG Measures;93
8.5;V. Spectral Gleason Measures;95
8.6;VI. Convergence of Gleason Measures;102
8.7;VII. Gleason Measures in Tensor Products;107
8.8;VIII. Random Gleason Measures;110
8.9;ACKNOWLEDGMENTS;116
8.10;REFERENCES;116
9;Chapter 3. An Introduction to Nonstandard Analysis and Hyperfinite Probability Theory;118
9.1;I. Introduction;118
9.2;II. An Introduction to Nonstandard Analysis;121
9.3;III. A Nonstandard Representation of Measurable Spaces and L8;136
9.4;IV. Conversion from Nonstandard to Standard Measure Spaces;141
9.5;V. Applications to Stochastic Processes;148
9.6;REFERENCES;154
10;Chapter 4. Limit Theorems: Stochastic Matrices, Ergodic Markov Chains, and Measures on Semigroups;156
10.1;I. Introduction and Preliminaries;156
10.2;II. Limits of Convolutions in Groups and Semigroups: Analysis in Stochastic Matrices;160
10.3;III. Ergodicity of Markov Chains and Probability Measures on Semigroups: An Interplay;176
10.4;IV. Limit Theorems for Convolution Products of Probability Measures on Completely Simple Semigroups;196
10.5;REFERENCES;214
11;Index;218