| Preface | | vii | |
| Introduction | | 1 | (8) |
| PART I. THEORY | | 9 | (158) |
| Chapter 1. Processes Discrete in Space and Time |
| | 9 | (48) |
| | 9 | (1) |
| 1.2 Fundamental Definitions and Properties |
| | 10 | (10) |
| 1.3 Calculation of Moments and Cumulants |
| | 20 | (3) |
| 1.4 The Fundamental Theorem Concerning Branching Processes |
| | 23 | (3) |
| 1.5 Remarks on the Number of Generations to Extinction |
| | 26 | (1) |
| | 27 | (16) |
| 1.7 Representation as Random-walk Processes |
| | 43 | (4) |
| 1.8 N-dimensional Branching Processes |
| | 47 | (4) |
| | 51 | (2) |
| | 53 | (4) |
| Chapter 2. Processes Discrete in Space and Continuous in Time |
| | 57 | (72) |
| | 57 | (1) |
| 2.2 Fundamental Equations of Discontinuous Markov Processes |
| | 57 | (4) |
| 2.3 Infinite Systems of Stochastic Differential Equations |
| | 61 | (11) |
| 2.4 Some Discontinuous Markov Processes and Their Properties |
| | 72 | (22) |
| 2.5 Age-dependent Branching Stochastic Processes |
| | 94 | (8) |
| | 102 | (16) |
| 2.7 N-dimensional Discontinuous Processes |
| | 118 | (3) |
| | 121 | (3) |
| | 124 | (5) |
| Chapter 3. Processes Continuous in Space and Time |
| | 129 | (38) |
| | 129 | (1) |
| 3.2 Diffusion Processes on the Real Line: The Theory of Kolmogorov |
| | 130 | (12) |
| 3.3 Diffusion Processes on the Real Line: The Theory of Feller |
| | 142 | (6) |
| 3.4 First-passage Time Problems for Diffusion Processes |
| | 148 | (6) |
| 3.5 Diffusion-equation Representation of Discrete Processes |
| | 154 | (4) |
| 3.6 N-dimensional Diffusion Processes |
| | 158 | (2) |
| | 160 | (2) |
| | 162 | (5) |
| PART II. APPLICATIONS | | 167 | (272) |
| Chapter 4. Applications in Biology |
| | 167 | (68) |
| | 167 | (1) |
| 4.2 Growth of Populations |
| | 168 | (24) |
| 4.3 Growth of Populations Subject to Mutation |
| | 192 | (6) |
| 4.4 Stochastic Theory of Epidemics |
| | 198 | (15) |
| 4.5 Diffusion Processes in the Theory of Gene Frequencies |
| | 213 | (10) |
| | 223 | (7) |
| | 230 | (5) |
| Chapter 5. Applications in Physics: Theory of Cascade Processes |
| | 235 | (60) |
| | 235 | (3) |
| 5.2 Electron-photon Cascades |
| | 238 | (27) |
| | 265 | (11) |
| | 276 | (6) |
| 5.5 The Ramakrishnan-Srinivasan Approach to Cascade Theory |
| | 282 | (5) |
| 5.6 Some Additional Studies on Cascade Processes |
| | 287 | (2) |
| | 289 | (6) |
| Chapter 6. Applications in Physics: Additional Applications |
| | 295 | (39) |
| | 295 | (1) |
| 6.2 Theory of Radioactive Transformations |
| | 295 | (4) |
| 6.3 Theory of Particle Counters |
| | 299 | (14) |
| 6.4 A Problem Concerning Nuclear Fission Detectors |
| | 313 | (4) |
| 6.5 Theory of Tracks in Nuclear Research Emulsions |
| | 317 | (6) |
| 6.6 Some Problems in the Theory of Nuclear Reactors |
| | 323 | (8) |
| | 331 | (3) |
| Chapter 7. Applications in Astronomy and Astrophysics |
| | 334 | (25) |
| | 334 | (1) |
| 7.2 Theory of Fluctuations in Brightness of the Milky Way |
| | 335 | (12) |
| 7.3 Theory of the Spatial Distribution of Galaxies |
| | 347 | (3) |
| 7.4 Stochastic Theory of Radiative Transfer |
| | 350 | (7) |
| | 357 | (2) |
| Chapter 8. Applications in Chemistry |
| | 359 | (15) |
| | 359 | (1) |
| 8.2 Some Stochastic Models for Chemical Reaction Kinetics |
| | 360 | (11) |
| 8.3 Remarks on Other Applications |
| | 371 | (1) |
| | 372 | (2) |
| Chapter 9. Applications in Operations Research: The Theory of Queues |
| | 374 | (65) |
| | 374 | (3) |
| 9.2 Representation of Queueing Processes. General Theory |
| | 377 | (18) |
| 9.3 Applications to Telephone Traffic Theory |
| | 395 | (12) |
| 9.4 Applications to the Servicing of Machines |
| | 407 | (18) |
| 9.5 Some Special Queueing Processes |
| | 425 | (9) |
| | 434 | (5) |
| APPENDIXES | | 439 | (20) |
| Appendix A Generating Functions | | 439 | (4) |
| Appendix B The Laplace and Mellin Transforms | | 443 | (6) |
| Appendix C Monte Carlo Methods in the Study of Stochastic Processes | | 449 | (10) |
| Name Index | | 459 | (5) |
| Subject Index | | 464 | |
