Synopses & Reviews
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.
Synopsis
This introduction to the theory of stochastic processes explains the fundamentals of the art of stochastic modeling. It covers Markov Chains with a countable state space, in both discrete and continuous time, finite Gibbs fields, non-homogeneous Markov chains, discrete time regenerative processes, Monte Carlo simulation, simulated annealing, and queueing networks. Applications-driven examples bring the reader to the very borders of contemporary research.
Synopsis
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 calculus, algebra, and number theory. A number of carefully chosen problems of varying difficulty are proposed at the close of each chapter, and the mathematics are slowly and carefully developed, in order to make self-study easier. The author treats the classic topics of Markov chain theory, both in discrete time and continuous time, as well as the connected topics such as finite Gibbs fields, nonhomogeneous Markov chains, discrete- time regenerative processes, Monte Carlo simulation, simulated annealing, and queuing theory. The result is an up-to-date textbook on stochastic processes. Students and researchers in operations research and electrical engineering, as well as in physics and biology, will find it very accessible and relevant.
Synopsis
Primarily an introduction to the theory of stochastic processes at the undergraduate or beginning graduate level, the primary objective of this book is to initiate students in the art of stochastic modelling. However it is motivated by significant applications and progressively brings the student to the borders of contemporary research. Examples are from a wide range of domains, including operations research and electrical engineering. Researchers and students in these areas as well as in physics, biology and the social sciences will find this book of interest.
Table of Contents
Preface * 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 * Appendix * Bibliography * Author Index * Subject Index