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Probabilistic Methods in Applied Mathematics
Volume 3
- 1st Edition - May 10, 2014
- Editor: A. T. Bharucha-Reid
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 3 6 1 9 - 3
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 7 6 1 2 - 0
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… Read more
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Request a sales quoteProbabilistic 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.
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
- No. of pages: 358
- Language: English
- Edition: 1
- Published: May 10, 2014
- Imprint: Academic Press
- Paperback ISBN: 9781483236193
- eBook ISBN: 9781483276120
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