Probabilistic Analysis and Related Topics
Volume 2
- 1st Edition - January 28, 1979
- Imprint: Academic Press
- Editor: A. T. Bharucha-Reid
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 3 6 1 7 - 9
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 7 5 5 3 - 6
Probabilistic Analysis and Related Topics, Volume 2 focuses on the integrability, continuity, and differentiability of random functions, as well as functional analysis, measure… Read more
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Request a sales quoteProbabilistic 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.
List of Contributors
Preface
Optimal Control of Stochastic Systems
I. Introduction
II. Existence of Optimal Controls without Feedback
III. Existence of Optimal Feedback Controls
IV. Random Necessary Conditions
V. Analytic Necessary Conditions
References
Gleason Measures
I. Introduction
II. Generalities
III. Orthogonally Scattered Gleason Measures
IV. L2ξ(H)-Spaces and Isometries Generated by OSG Measures
V. Spectral Gleason Measures
VI. Convergence of Gleason Measures
VII. Gleason Measures in Tensor Products
VIII. Random Gleason Measures
References
An Introduction to Nonstandard Analysis and Hyperfinite Probability Theory
I. Introduction
II. An Introduction to Nonstandard Analysis
III. A Nonstandard Representation of Measurable Spaces and L∞
IV. Conversion from Nonstandard to Standard Measure Spaces
V. Applications to Stochastic Processes
References
Limit Theorems: Stochastic Matrices, Ergodic Markov Chains, and Measures on Semigroups
I. Introduction and Preliminaries
II. Limits of Convolutions in Groups and Semigroups: Analysis in Stochastic Matrices
III. Ergodicity of Markov Chains and Probability Measures on Semigroups: An Interplay
IV. Limit Theorems for Convolution Products of Probability Measures on Completely Simple Semigroups
References
Index
- Edition: 1
- Published: January 28, 1979
- No. of pages (eBook): 220
- Imprint: Academic Press
- Language: English
- Paperback ISBN: 9781483236179
- eBook ISBN: 9781483275536
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