Probabilistic Analysis and Related Topics

List of Contributors

Preface

Qualitative Theory of Stochastic Systems

I. Introduction

II. Scope of the Theory

III. Nonlinear Systems

IV. Linear Systems

V. Linearization

VI. Generalizations

VII. Applications

References

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

References

Stability Theory of Stochastic Difference Systems

I. Introduction

II. Linear Stochastic Systems

III. Stochastic Stability of Nonlinear Systems

IV. Directions for Further Research

References

Markov Properties for Random Fields

Introduction

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

References

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

References

Index