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Elements of the Theory of Markov Processes and Their Applications

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Elements of the Theory of Markov Processes and Their Applications Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

Graduate-level text and reference in probability, with numerous scientific applications. Nonmeasure-theoretic introduction to theory of Markov processes and to mathematical models based on the theory. 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

Product Details

ISBN:
9780486695396
Author:
Bharucha-Reid, A. T.
Author:
Bharucha-Reid, Albert T.
Author:
Bharucha-Reid
Author:
Bharucha-Reid, A. T.
Author:
Mathematics
Publisher:
Dover Publications
Location:
Mineola, N.Y. :
Subject:
Mathematics
Subject:
Probability
Subject:
Markov processes
Subject:
Probability & Statistics - General
Subject:
General Mathematics
Subject:
Statistics
Subject:
Mathematics | Probability and Statistics
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
20101031
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
480
Dimensions:
8.5 x 5.38 in 1.22 pd

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Product details 480 pages Dover Publications - English 9780486695396 Reviews:
"Synopsis" by ,
Graduate-level text and reference in probability, with numerous scientific applications. Nonmeasure-theoretic introduction to theory of Markov processes and to mathematical models based on the theory. Appendixes. Bibliographies. 1960 edition.
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