Probabilistic Analysis and Related Topics

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