Bharucha-Reid Probabilistic Methods in Applied Mathematics

Volume 3
1. Auflage 2014
ISBN: 978-1-4832-7612-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 358 Seiten, Web PDF

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.

Autoren/Hrsg.

Bharucha-Reid, A. T.

Inhaltsverzeichnis

1;Front Cover;1
2;Probabilistic Methods in Applied Mathematics;4
3;Copyright Page;5
4;Table of Contents;6
5;List of Contributors;8
6;Preface;10
7;Contents of Other Volumes;12
8;CHAPTER 1. STATISTICALLY WELL-SET CAUCHY PROBLEMS;14
8.1;I. Introduction;15
8.2;II. Probability in Function Spaces;26
8.3;III. Well-Set Cauchy Problems;40
8.4;IV. Some Special Conditions;51
8.5;V. Correlation and Spectrum;62
8.6;VI. Evolution of the Spectral Matrix Measure;88
8.7;VII. Parabolic Problems;99
8.8;Appendix A: Borel Sets in the Relevant Function Spaces;108
8.9;Appendix B: Regular Probability Measures;115
8.10;Appendix C: Cauchy Problems Which Are Statistically but Not Deterministically Well Set;123
8.11;Appendix D: Existence of Normal Measures with Given Covariance;128
8.12;Acknowledgements;131
8.13;References;131
9;CHAPTER 2. WAVE PROPAGATION IN RANDOM ANISOTROPIC MEDIA;134
9.1;I. Introduction;135
9.2;II. Mathematical Techniques;140
9.3;III. An Effective Medium Description for a Random Uniaxial Anisotropic Medium and the Resulting Dyadic Green's Function;168
9.4;IV. Extension to Biaxial Anisotropic Random Media;184
9.5;V. Summary;188
9.6;Appendix: Evaluation of Ko(k);189
9.7;Acknowledgements;190
9.8;References;190
10;CHAPTER 3. STOCHASTIC PROCESSES IN HEAT AND MASS TRANSPORT;196
10.1;I. Introduction;196
10.2;II. Velocity Field;197
10.3;III. Mass Transport;207
10.4;IV. Temperature Transport;219
10.5;V. Coupling of Mass and Heat Transport;220
10.6;VI. Conclusion;222
10.7;References;222
11;CHAPTER 4. POTENTIAL THEORY FOR MARKOV CHAINS;226
11.1;Introduction;227
11.2;I. Markov Chains;229
11.3;II. Potential Theory for a Transient Kernel;231
11.4;III. Hitting Distributions;236
11.5;IV. Dirichlet Problem and Poisson Equation;245
11.6;V. Martingales and Potentials;249
11.7;VI. Problems of Potential Theory;256
11.8;VII. Martin Boundary;264
11.9;VIII. Examples;275
11.10;Appendixes;285
11.11;References;288
12;CHAPTER 5. ON SOME STOCHASTIC DIFFERENTIAL GAMES;290
12.1;I. Preliminary Concepts;291
12.2;II. The Solution of a General Stochastic Linear Pursuit-Evasion Game;309
12.3;III. The Solution of a Stochastic Linear Pursuit-Evasion Game with Nonrandom Controls;317
12.4;IV. Formal Solutions for Some Classes of Stochastic Linear Pursuit-Evasion Games;330
12.5;V. Many-Player Stochastic Differential Games;335
12.6;References;346
13;Author Index;350
14;Subject Index;355