Elements of the Theory of Markov Processes and Their Applications
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.
1 online resource (914 p.).
9780486150352, 0486150356
1162446174
""Cover""; ""Title Page""; ""Copyright Page""; ""Dedication""; ""Preface""; ""Contents""; ""Introduction""; ""Part I. 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 Concerning Branching Processes""; ""1.5 Remarks on the Number of Generations to Extinction""; ""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 Processes on the Real Line : The Theory of Kolmogorov"" ""3.3 Diffusion Processes 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""; ""Bibliography""; ""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""
Description based upon print version of record
""9.1 Introduction""
English