Probabilistic Analysis and Related Topics

List of Contributors

Preface

Stochastic Partial Differential Equations in Turbulence Related Problems

I. Introduction

II. Theory of Stochastic Partial Differential Equations

III. Linear Stochastic Partial Differential Equations in Weak Turbulence

IV. Partial Differential Equations in Stochastic Wave Propagation

V. Stochastic Equations in Turbulent Transport Theory

VI. Markovian Model Equations in Turbulence

References

Estimation and Stochastic Control for Linear Infinite-Dimensional Systems

I. Introduction

II. The Semigroup Description of Linear Autonomous Systems

III. Stochastic Evolution Equations

IV. Deterministic Quadratic Cost-Control Problem

V. State Estimation

VI. The Separation Principle for Stochastic Optimal Control

VII. Extensions

References

Random Integrodifferential Equations

I. Introduction and Preliminaries

II. Existence and Uniqueness of Solution

III. Some Stochastic Properties of Solution Processes

IV. Small Perturbations

V. Vibrating String

References

Equivalence and Singularity of Gaussian Measures and Applications

I. Introduction

II. General Problem of Equivalence and Singularity

III. Reproducing Kernel Hilbert Spaces and Gaussian Processes

IV. Equivalence and Singularity of Gaussian Processes

V. Conditions for Equivalence: Special Cases

VI. Applications

VII. Concluding Remarks

Appendix

References

Stochastic Riemannian Geometry

I. Introduction

II. Brownian Motion

III. Semilocal Properties

IV. Asymptotic Properties, t → 0

V. Asymptotic Properties, t → ∞

VI. Bibliographical Remarks

References

Index