Adomian Applied Stochastic Processes

1. Auflage 2014
ISBN: 978-1-4832-5908-6
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 312 Seiten, Web PDF

Applied Stochastic Processes is a collection of papers dealing with stochastic processes, stochastic equations, and their applications in many fields of science. One paper discusses stochastic systems involving randomness in the system itself that can be a large dynamical multi-input, multi-output system. Examples of a large system are the national economy of a major country or when an acoustic wave is propagating as in the atmosphere, ocean, or sea. Another paper proves that only the average properties of the molecules of biology can be measured with precision in the test tube; and disputes a 'simplistic' model of the cell as defined by a miniature Laplaces' universe. The paper notes that the way existing cells are constructed implies that quantum mechanical principles lead to certain questions (about simple experiments) having only statistical answers. Another paper addresses the detection of distributed, fluctuating targets in a reverberation limited, randomly time, and space varying transmission media. This approach is done by using the concepts of 'random Green's functions' and the 'stochastic Green's function.' The collection will prove useful for cellular researchers, mathematicians, physicist, engineers, and academicians in the field of applied mathematics, statistics, and chemistry.

Autoren/Hrsg.

Adomian, G.

Inhaltsverzeichnis

1;Front Cover;1
2;Applied Stochastic Processes;4
3;Copyright Page;5
4;Table of Contents;6
5;CONTRIBUTORS;8
6;PREFACE;10
7;CHAPTER 1. STOCHASTIC SYSTEMS ANALYSIS;12
7.1;I. INTRODUCTION;12
7.2;II. NONLINEAR STOCHASTIC SYSTEMS;13
7.3;III. FORMS OF Ny;17
7.4;IV. APPLICATION TO LINEAR DETERMINISTIC PARTIAL DIFFERENTIAL EQUATIONS;21
7.5;V. LINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS;22
7.6;VI. LINEAR STOCHASTIC DIFFERENTIAL EQUATION;23
7.7;VII. NONLINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS;24
7.8;VIII. CONCLUSIONS;27
7.9;REFERENCES;28
8;CHAPTER 2. VARIATIONAL FORMULATION OF SOME PROBLEMS FOR THE RANDOM HEAT EQUATION;30
8.1;1. INTRODUCTION;30
8.2;2. PRELIMINARIES: NOTATION, DEFINITIONS;35
8.3;3. A RANDOM ABSTRACT EVOLUTION EQUATION: VARIATIONAL FORMULATION;38
8.4;4. APPLICATION TO THE RANDOM HEAT EQUATION;42
8.5;5. COMMENTS AND EXTENSIONS;44
8.6;REFERENCES;45
9;CHAPTER 3. LIMITATIONS ON DETERMINISM AT THE CELLULAR LEVEL IN BIOLOGY DUE TO VARIABILITY AT THE MOLECULAR LEVEL;48
9.1;INTRODUCTION;48
9.2;DEFINITION OF LIFE;50
9.3;QUANTUM INTERVENTION;55
9.4;THERMAL FLUCTUATIONS;58
9.5;AN EXPERIMENTALLY OBSERVABLE VARIATION IN A MICROSCOPIC PARAMETER;61
9.6;VARIANCE AT THE POPULATION LEVEL AS A FUNCTION OF MOLECULAR FLUCTUATIONS;69
9.7;SUMMARY;75
9.8;ACKNOWLEDGMENTS;75
9.9;REFERENCES;76
10;CHAPTER 4. SOME RANDOM BOUNDARY PROBLEMS IN TWO DIMENSIONS;82
10.1;INTRODUCTION;82
10.2;2. REDUCED WAVE EQUATION IN A RANDOM DOMAIN;84
10.3;3. ANALYSIS OF A PROBABILISTIC MODEL;87
10.4;REFERENCES;92
11;CHAPTER 5. COMPETITIVE-COOPERATIVE PROCESSES AND STABILITY OF DIFFUSION SYSTEMS;94
11.1;1. INTRODUCTION;94
11.2;2. LINEAR DIFFUSION COMPETITIVE SYSTEMS;95
11.3;3. NONLINEAR DIFFUSION COMPETITIVE SYSTEMS;102
11.4;4. HIERARCHIC DIFFUSION COMPETITIVE SYSTEMS;110
11.5;5. EXAMPLES;114
11.6;REFERENCES;117
12;CHAPTER 6. STOCHASTIC DIFFERENTIAL INEQUALITIES OF Itô TYPE;120
12.1;1. INTRODUCTION;120
12.2;2. NOTATIONS AND DEFINITIONS;121
12.3;3. NONNEGATIVITY OF SOLUTIONS OF Itô SYSTEMS;121
12.4;4. STOCHASTIC DIFFERENTIAL INEQUALITIES;125
12.5;5. MAXIMAL AND MINIMAL SOLUTIONS;128
12.6;6. COMPARISON THEOREMS;130
12.7;REFERENCES;131
13;CHAPTER 7. APPROXIMATE SOLUTION OF RANDOM DIFFERENTIAL AND INTEGRAL EQUATIONS;132
13.1;2. PERTURBATION TECHNIQUES;133
13.2;3. HIERARCHY TECHNIQUES;135
13.3;4. STOCHASTIC GREEN'S FUNCTION APPROACH;136
13.4;5. REDUCTION TO DETERMINISTIC PARTIAL DIFFERENTIAL EQUATIONS;137
13.5;6. NUMERICAL METHODS;138
13.6;7. SUCCESSIVE APPROXIMATION AND STOCHASTIC APPROXIMATION TECHNIQUES;140
13.7;8. METHOD OF MOMENTS;141
13.8;9. SUMMARY;142
13.9;REFERENCES;143
14;CHAPTER 8. A SURVEY OF STOCHASTIC MODELS FOR BOD AND DO IN STREAMS;146
14.1;INTRODUCTION;146
14.2;2. BASIC DETERMINISTIC MODELS;147
14.3;3. STOCHASTIC MODELS FOR BOD AND DO;149
14.4;REFERENCES;158
15;CHAPTER 9. SOLUTIONS OF PHYSICAL STOCHASTIC PROCESSES VIA MAPPINGS ONTO IDEAL AND DEFECTIVE RANDOM WALK LATTICES;162
15.1;1. INTRODUCTION;162
15.2;2. MATHEMATICAL FORMALISM: MULTISTATE LATTICES;165
15.3;3. MULTISTATE RANDOM WALKS: FIM;174
15.4;4. ON MECHANISMS OF VACANCY DIFFUSION;187
15.5;5. TIME DEPENDENT CORRELATED MOTION;193
15.6;6. FLUX THROUGH NEURAL MEMBRANES;196
15.7;7. MATHEMATICAL FORMALISM: DEFECT RENORMALIZED PROPAGATORS;197
15.8;8. QUASI-ELASTIC NEUTRON SCATTERING FROM DIFFUSING SPECIES;219
15.9;9. UNIMOLECULAR REACTIONS;224
15.10;10. BIMOLECULAR REACTIONS;235
15.11;11. CONCLUSIONS;240
15.12;APPENDIX A: Partial Discrete Fourier Transforms;243
15.13;APPENDIX B: The Mean and Variance: Shortcuts;245
15.14;APPENDIX C: Ladder Climbing;250
15.15;REFERENCES;253
16;CHAPTER 10. OPTIMUM DETECTION AND ESTIMATION IN STOCHASTIC TRANSMISSION MEDIA;258
16.1;INTRODUCTION;258
16.2;RANDOM AND STOCHASTIC GREEN'S FUNCTIONS;259
16.3;SCATTERING FUNCTIONS;262
16.4;PARAMETER ESTIMATION;268
16.5;DETECTION;270
16.6;DISCUSSION AND CONCLUSIONS;274
16.7;ACKNOWLEDGMENT;276
16.8;REFERENCES;276
17;CHAPTER 11. RECENT DEVELOPMENTS IN NONPARAMETRIC ESTIMATION OF PROBABILITY DENSITY;280
17.1;INTRODUCTION;280
17.2;NEW RESULTS ON KERNEL ESTIMATORS;281
17.3;3. APPLICATIONS TO REGRESSSION ANALYSIS;284
17.4;4.0 MAXIMUM PENALIZED LIKELIHOOD ESTIMATORS;289
17.5;REFERENCES;290
18;CHAPTER 12. ON DISSIPATIVE NONLINEAR HAMILTONIAN SYSTEMS;294
18.1;1. INTRODUCTION;294
18.2;2. MEAN SQUARE LINEARIZATION;297
18.3;3. LINEARIZATION BY TRANSFORMATION;301
18.4;4. CONCLUSIONS;309
18.5;ACKNOWLEDGMENTS;311
18.6;REFERENCES;311