Probabilistic Analysis and Related Topics

Probabilistic Analysis and Related Topics

Volume 2

1st Edition - January 28, 1979

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  • Editor: A. T. Bharucha-Reid
  • eBook ISBN: 9781483275536

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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.

Table of Contents

  • List of Contributors


    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


    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


    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


    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



Product details

  • No. of pages: 220
  • Language: English
  • Copyright: © Academic Press 1979
  • Published: January 28, 1979
  • Imprint: Academic Press
  • eBook ISBN: 9781483275536

About the Editor

A. T. Bharucha-Reid

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