Probabilistic Analysis and Related Topics - 1st Edition - ISBN: 9780120956012, 9781483276656

Probabilistic Analysis and Related Topics

1st Edition

Volume 1

Editors: A. T. Bharucha-Reid
eBook ISBN: 9781483276656
Imprint: Academic Press
Published Date: 28th January 1978
Page Count: 250
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Description

Probabilistic Analysis and Related Topics, Volume 1 focuses on the continuity, differentiability, and integrability of random functions, including functional analysis, operator theory, measure theory, and numerical analysis.

The selection first offers information on stochastic partial differential equations in turbulence related problems and estimation and stochastic control for linear infinite-dimensional systems. Discussions focus on deterministic quadratic cost-control problem; partial differential equations in stochastic wave propagation; and theory of stochastic partial differential equations. The text then examines random integrodifferential equations, including small perturbations, existence and uniqueness of solutions, stochastic properties of solution processes, and vibration string.

The manuscript ponders on equivalence and singularity of Gaussian measures and applications and stochastic Riemannian geometry. Concerns include semilocal properties, Brownian motion, reproducing kernel Hilbert spaces and Gaussian processes, equivalence and singularity of Gaussian processes, and general problem of equivalence and singularity.

The selection is a vital source of information for mathematicians and researchers interested in the general theory of random functions.

Table of Contents


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

Details

No. of pages:
250
Language:
English
Copyright:
© Academic Press 1978
Published:
Imprint:
Academic Press
eBook ISBN:
9781483276656

About the Editor

A. T. Bharucha-Reid