Elements of the Theory of Markov Processes and Their Applications: (Dover Books on Mathematics)

This graduate-level text and reference in probability, with numerous applications to several fields of science, presents nonmeasure-theoretic introduction to theory of Markov processes. The work also covers mathematical models based on the theory, employed in various applied fields. Prerequisites are a knowledge of elementary probability theory, mathematical statistics, and analysis. Appendixes. Bibliographies. 1960 edition.

Table of Contents:
Preface Introduction PART 1. THEORY Chapter 1. Processes Discrete in Space and Time 1.1 Introduction 1.2 Fundamental Definitions and Properties 1.3 Calculation of Moments and Cumulants 1.4 The Fundamental Theorem Concenling Branching Processes 1.5 Remarks on the Number of Generations to Extinetion 1.6 Limit Theorems 1.7 Representation as Random-walk Processes 1.8 N -dimensional Branching Processes Problems Bibliography Chapter 2. Processes Discrete in Space and Continuous in Time 2.1 Introduction 2.2 Fundamental Equations of Discontinuous Markov Processes 2.3 Infinite Systems of Stochastic Differential Equations 2.4 Some Discontinuous Markov Processes and Their Properties 2.5 Age-dependent Branching Stochastic Processes 2.6 Limit Theorems 2.7 N -dimensional Discontinuous Processes Problems Bibliography Chapter 3. Processes Continuous in Space and Time 3.1 Introduction 3.2 Diffusion Proccesses on the Real Line: The Theory of Kolmogorov 3.3 Diffusion Proccesses on the Real Line: The Theory of Feller 3.4 First-passage Time Problems for Diffusion Processes 3.5 Diffusion-equation Representation of Discrete Processes 3.6 N-dimensional Diffusion Processes Problems Bibliography PART II. APPLICATIONS Chapter 4. Applications in Biology 4.1 Introduction 4.2 Growth of Populations 4.3 Growth of Populations Subject to Mutation 4.4 Stochastic Theory of Epidemics 4.5 Diffusion Processes in the Theory of Gene Frequencies 4.6 Radiobiology Bibliography Chapter 5. Applications in Physics: Theory of Cascade Processes 5.1 Introduction 5.2 Electron-photon Cascades 5.3 Nucleon Cascades 5.4 Ionization Cascades 5.5 The Ramakrishnan-Srinivasan Approach to Cascade Theory 5.6 Some Additional Studies on Cascade Processes Chapter 6. Applications in Physics: Additional Applications 6.1 Introduction 6.2 Theory of Radioactive Transformations 6.3 Theory of Particle Counters 6.4 A Problem Concerning Nuclear Fission Detectors 6.5 Theory of Tracks in Nuclear Research Emulsions 6.6 Some Problems in the Theory of Nuclear Reactors Bibliography Chapter 7. Applications in Astronomy and Astrophysics 7.1 Introduction 7.2 Theory of Fluctuations in Brightness of the Milky Way 7.3 Theory of the Spatial Distribution of Galaxies 7.4 Stochastic Theory of Radiative Transfer Bibliography Chapter 8. Applications in Chemistry 8.1 Introduction 8.2 Some Stochastic Models for Chemical Reaction Kinetics 8.3 Remarks on Other Applications Bibliography Chapter 9. Applications in Operations Research: The Theory of Queues 9.1 Introduction 9.2 Representation of Queueing Processes. General Theory 9.3 Applications to Telephone Traffic Theory 9.4 Applications to the Servicing of Machines 9.5 Some Special Queueing Processes Bibliography APPENDIXES Appendix A Generating Functions Appendix B The Laplace and Mellin Transforms Appendix C Monte Carlo Methods in the Study of Stochastic Processes Name Index Subject Index