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Probabilistic Analysis and Related Topics - 1st Edition - ISBN: 9780120956036, 9781483275468

Probabilistic Analysis and Related Topics

1st Edition

Volume 3

Editor: A. T. Bharucha-Reid
eBook ISBN: 9781483275468
Imprint: Academic Press
Published Date: 28th January 1983
Page Count: 270
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Probabilistic Analysis and Related Topics, Volume 3 focuses on the continuity, integrability, and differentiability of random functions, including operator theory, measure theory, and functional and numerical analysis.

The selection first offers information on the qualitative theory of stochastic systems and Langevin equations with multiplicative noise. Discussions focus on phase-space evolution via direct integration, phase-space evolution, linear and nonlinear systems, linearization, and generalizations. The text then ponders on the stability theory of stochastic difference systems and Markov properties for random fields. Topics include Markov property of solutions of stochastic partial differential equations; Markov property for generalized Gaussian random fields; Markov properties for generalized random fields; stochastic stability of nonlinear systems; and linear stochastic systems.

The publication examines the method of random contractors and its applications to random nonlinear equations, including integral contractors and applications to random equations; random contractors with random nonlinear majorant functions; and random contractors and application to random nonlinear operator equations.

The selection is a valuable reference for mathematicians and researchers interested in the general theory of random functions.

Table of Contents

List of Contributors


Qualitative Theory of Stochastic Systems

I. Introduction

II. Scope of the Theory

III. Nonlinear Systems

IV. Linear Systems

V. Linearization

VI. Generalizations

VII. Applications


Langevin Equations with Multiplicative Noise: Theory and Applications to Physical Processes

I. Introduction

II. Phase-Space Evolution: Cumulant Expansion Technique (Stratonovich)

III. Phase-Space Evolution via Direct Integration (Itô and Stratonovich)

IV. Examples


Stability Theory of Stochastic Difference Systems

I. Introduction

II. Linear Stochastic Systems

III. Stochastic Stability of Nonlinear Systems

IV. Directions for Further Research


Markov Properties for Random Fields


I. Conditional Independence and Its Consequences

II. Markov Properties for Multiparameter Processes

III. Markov Property on a Class of Sets

IV. Markov Properties for Generalized Random Fields

V. Quasi-Invariant Measures and the Markov Property

VI. Markov Property for Generalized Gaussian Random Fields

VII. Markov Property for Solutions of Stochastic Partial Differential Equations

Appendix A: Gaussian Processes and Reproducing Kernel Spaces

Appendix B: Generalized Gaussian Random Field


The Method of Random Contractors and Its Applications to Random Nonlinear Equations

I. Introduction

II. Contractors and Deterministic Nonlinear Operators

III. Preliminary Definitions

IV. Random Contractors and Application to Random Nonlinear Operator Equations

V. Random Contractors with Random Nonlinear Majorant Functions

VI. Random Step-Contractors

VII. Integral Contractors and Applications to Random Equations




No. of pages:
© Academic Press 1983
28th January 1983
Academic Press
eBook ISBN:

About the Editor

A. T. Bharucha-Reid

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