Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues

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Springer Science & Business Media, Mar 9, 2013 - Mathematics - 444 pages
This book discusses both the theory and applications of Markov chains. The author studies both discrete-time and continuous-time chains and connected topics such as finite Gibbs fields, non-homogeneous Markov chains, discrete time regenerative processes, Monte Carlo simulation, simulated annealing, and queueing networks are also developed in this accessible and self-contained text. The text is firstly an introduction to the theory of stochastic processes at the undergraduate or beginning graduate level. Its primary objective is to initiate the student to the art of stochastic modelling. The treatment is mathematical, with definitions, theorems, proofs and a number of classroom examples which help the student to fully grasp the content of the main results. Problems of varying difficulty are proposed at the close of each chapter. The text is motivated by significant applications and progressively brings the student to the borders of contemporary research. Students and researchers in operations research and electrical engineering as well as in physics, biology and the social sciences will find this book of interest.
 

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Contents

Probability Review
1
DiscreteTime Markov Models
53
Recurrence and Ergodicity
95
Long Run Behavior
125
Lyapunov Functions and Martingales
167
Eigenvalues and Nonhomogeneous Markov Chains
195
Gibbs Fields and Monte Carlo Simulation
253
Bayesian Restoration of Images
275
ContinuousTime Markov Models
323
Poisson Calculus and Queues
369
Appendix
417
Bibliography
433
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