Probabilistic Analysis and Related Topics

Probabilistic Analysis and Related Topics

Volume 1

1st Edition - January 28, 1978

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  • Editor: A. T. Bharucha-Reid
  • eBook ISBN: 9781483276656

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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


    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


    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


    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


    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



    Stochastic Riemannian Geometry

    I. Introduction

    II. Brownian Motion

    III. Semilocal Properties

    IV. Asymptotic Properties, t → 0

    V. Asymptotic Properties, t → ∞

    VI. Bibliographical Remarks



Product details

  • No. of pages: 250
  • Language: English
  • Copyright: © Academic Press 1978
  • Published: January 28, 1978
  • Imprint: Academic Press
  • eBook ISBN: 9781483276656

About the Editor

A. T. Bharucha-Reid

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