Finite Markov processes and their applications /

Finite Markov processes and their applications /

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Bibliographic Details
Author / Creator:Iosifescu, Marius
Uniform title:Lanțuri Markov finite și aplicații. English.
Edition:[Rev. and expanded ed.].
Imprint:Chichester ; New York : J. Wiley, c1980.
Description:295 p. ; 23 cm.
Language:English
Romanian
Series:Wiley series in probability and mathematical statistics
Wiley series in probability and mathematical statistics
Subject:Markov processes
Markov processes.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/502638
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ISBN:0471276774 : $32.50
Notes:Rev. and expanded translation of Lanțuri Markov finite și aplicații.
Includes index.
Bibliography: p. [275]-289.
Table of Contents:
  • Introduction
  • 1.8. r-dimensional space
  • 1.9. Eigenvalues and eigenvectors
  • 1.10. Nonnegative matrices. The Perron-Frobenius theorems
  • 1.11. Stochastic matrices. Ergodicity coefficients
  • Chapter 2. Fundamental Concepts in Homogeneous Markov Chain Theory
  • 2.1. The Markov property
  • 2.2. Examples of homogeneous Markov chains
  • 2.3. Stopping times and the strong Markov property
  • 2.4. Classes of states
  • 2.5. Recurrence and transience
  • Chapter 1. Elements of Probability Theory and Linear Algebra
  • 2.6. Classification of homogeneous Markov chains
  • Exercises
  • Chapter 3. Absorbing Markov Chains
  • 3.1. The fundamental matrix
  • 3.2. Applications of the fundamental matrix
  • 3.3. Extensions and complements
  • 3.4. Conditional transient behaviour
  • Exercises
  • Chapter 4. Ergodic Markov Chains
  • 4.1. Regular Markov chains
  • 1.1. Random events
  • 4.2. The stationary distribution
  • 4.3. The fundamental matrix
  • 4.4. Cyclic Markov chains
  • 4.5. Reversed Markov chains
  • 4.6. The Ehrenfest model
  • Exercises
  • Chapter 5. General Properties of Markov Chains
  • 5.1. Asymptotic behaviour of transition probabilities
  • 5.2. The tail [sigma]- algebra
  • 5.3. Limit theorems for partial sums
  • 1.2. Probability
  • 5.4. Grouped Markov chains
  • 5.5. Expanded Markov chains
  • 5.6. Extending the concept of a homogeneous finite Markov chain
  • Exercises
  • Chapter 6. Applications of Markov Chains in Psychology and Genetics
  • 6.1. Mathematical learning theory
  • 6.2. The pattern model
  • 6.3. The Markov chain associated with the pattern model
  • 6.4. The Mendelian theory of inheritance
  • 6.5. Sib mating
  • 1.3. Dependence and independence
  • 6.6. Genetic drift. The Wright model
  • Exercises
  • Chapter 7. Nonhomogeneous Markov Chains
  • 7.1. Generalities
  • 7.2. Weak ergodicity
  • 7.3. Uniform weak ergodicity
  • 7.4. Strong ergodicity
  • 7.5. Uniform strong ergodicity
  • 7.6. Asymptotic behaviour of nonhomogeneous Markov chains
  • Exercises
  • 1.4. Random variables. Mean values
  • Chapter 8. Markov Processes
  • 8.1. Measure theoretical definition of a Markov process
  • 8.2. The intensity matrix
  • 8.3. Constructive definition of a Markov process
  • 8.4. Discrete skeletons and classification of states
  • 8.5. Absorbing Markov processes
  • 8.6. Regular Markov processes
  • 8.7. Birth and death processes
  • 8.8. Extending the concept of a homogeneous finite Markov process
  • 8.9. Nonhomogeneous Markov processes
  • 1.5. Random processes
  • Exercises
  • Historical Notes
  • Bibliography
  • List of Symbols
  • Subject Index
  • 1.6.. Matrices
  • 1.7. Operations with matrices
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