Probabilistic Methods in Applied Mathematics

List of Contributors

Preface

Contents of Other Volumes

Statistically Well-Set Cauchy Problems

I Introduction

II Probability in Function Spaces

III Well-Set Cauchy Problems

IV Some Special Conditions

V Correlation and Spectrum

VI Evolution of the Spectral Matrix Measure

VII Parabolic Problems

Appendix A: Borel Sets in the Relevant Function Spaces

Appendix B: Regular Probability Measures

Appendix C: Cauchy Problems Which Are Statistically but Not Deterministically Well Set

Appendix D: Existence of Normal Measures with Given Covariance

References

Wave Propagation In Random Anisotropic Media

I Introduction

II Mathematical Techniques

III An Effective Medium Description for a Random Uniaxial Anisotropic Medium and the Resulting Dyadic Green's Function

IV Extension to Biaxial Anisotropic Random Media

V Summary

Appendix: Evaluation of K0(k)

References

Stochastic Processes In Heat And Mass Transport

I Introduction

II Velocity Field

III Mass Transport

IV Temperature Transport

V Coupling of Mass and Heat Transport

VI Conclusion

References

Potential Theory For Markov Chains

Introduction

I Markov Chains

II Potential Theory for a Transient Kernel

III Hitting Distributions

IV Dirichlet Problem and Poisson Equation

V Martingales and Potentials

VI Problems of Potential Theory

VII Martin Boundary

VIII Examples

Appendixes

References

On Some Stochastic Differential Games

I Preliminary Concepts

II The Solution of a General Stochastic Linear Pursuit-Evasion Game

III The Solution of a Stochastic Linear Pursuit-Evasion Game with Nonrandom Controls

IV Formal Solutions for Some Classes of Stochastic Linear Pursuit-Evasion Games

V Many-Player Stochastic Differential Games

References

Author Index

Subject Index