Probabilistic Methods in Applied Mathematics - 1st Edition - ISBN: 9780120957033, 9781483276120

Probabilistic Methods in Applied Mathematics

1st Edition

Volume 3

Editors: A. T. Bharucha-Reid
eBook ISBN: 9781483276120
Imprint: Academic Press
Published Date: 28th January 1973
Page Count: 358
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Description

Probabilistic Methods in Applied Mathematics, Volume 3 focuses on the influence of the probability theory on the formulation of mathematical models and development of theories in many applied fields.

The selection first offers information on statistically well-set Cauchy problems and wave propagation in random anisotropic media. Discussions focus on extension to biaxial anisotropic random media; an effective medium description for a random uniaxial anisotropic medium and the resulting dyadic Green's function; evolution of the spectral matrix measure; and well-set Cauchy problems. The text then examines stochastic processes in heat and mass transport, including mass transport, velocity field, temperature transport, and coupling of mass and heat transport.

The manuscript takes a look at the potential theory for Markov chains and stochastic differential games. Topics include formal solutions for some classes of stochastic linear pursuit-evasion games; solution of a stochastic linear pursuit-evasion game with nonrandom controls; problems of potential theory; and hitting distributions.

The selection is a vital source of data for mathematicians and researchers interested in the probability theory.

Table of Contents


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

Details

No. of pages:
358
Language:
English
Copyright:
© Academic Press 1973
Published:
Imprint:
Academic Press
eBook ISBN:
9781483276120

About the Editor

A. T. Bharucha-Reid