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Markov Chains Gibbs Fields, Monte Carlo Simulation, and Queues

In this book, the author begins with the elementary theory of Markov chains and very progressively brings the reader to the more advanced topics. He gives a useful review of probability that makes the book self-contained, and provides an appendix with detailed proofs of all the prerequisites from ca...

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Bibliographic Details
Main Author: Bremaud, Pierre
Format: eBook
Language:English
Published: New York, NY Springer New York 1999, 1999
Edition:1st ed. 1999
Series:Texts in Applied Mathematics
Subjects:
Operations Research
Electrical And Electronic Engineering
Electrical Engineering
Probability Theory
Operations Research And Decision Theory
Probabilities
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 1 Probability Review
  • 2 Discrete-Time Markov Models
  • 3 Recurrence and Ergodicity
  • 4 Long Run Behavior
  • 5 Lyapunov Functions and Martingales
  • 6 Eigenvalues and Nonhomogeneous Markov Chains
  • 7 Gibbs Fields and Monte Carlo Simulation
  • 8 Continuous-Time Markov Models
  • 9 Poisson Calculus and Queues
  • 1 Number Theory and Calculus
  • 1.1 Greatest Common Divisor
  • 1.2 Abel’s Theorem
  • 1.3 Lebesgue’s Theorems for Series
  • 1.4 Infinite Products
  • 1.5 Tychonov’s Theorem
  • 1.6 Subadditive Functions
  • 2 Linear Algebra
  • 2.1 Eigenvalues and Eigenvectors
  • 2.2 Exponential of a Matrix
  • 2.3 Gershgorin’s Bound
  • 3 Probability
  • 3.1 Expectation Revisited
  • 3.2 Lebesgue’s Theorems for Expectation
  • Author Index

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