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Texts in Applied Mathematics Ser.: Markov Chains : Gibbs Fields, Monte Carlo Simulation, and Queues by Pierre Bremaud (1999, Hardcover)
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About this product
Product Identifiers
PublisherSpringer New York
ISBN-100387985093
ISBN-139780387985091
eBay Product ID (ePID)1010306
Product Key Features
Number of PagesXviii, 444 Pages
Publication NameMarkov Chains : Gibbs Fields, Monte Carlo Simulation, and Queues
LanguageEnglish
SubjectProbability & Statistics / Stochastic Processes, Probability & Statistics / General, Operations Research, Electrical
Publication Year1999
TypeTextbook
Subject AreaMathematics, Technology & Engineering, Business & Economics
AuthorPierre Bremaud
SeriesTexts in Applied Mathematics Ser.
FormatHardcover
Dimensions
Item Height0.5 in
Item Weight38.9 Oz
Item Length9.4 in
Item Width6.3 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN98-017539
Dewey Edition22
Series Volume Number31
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal519.233
Table Of Content1 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.
SynopsisThis book begins with the elementary theory of Markov chains and very progressively brings the reader to the more advanced topics. The mathematics are carefully developed, making self-study easier. A number of carefully chosen problems of varying difficulty are proposed at the close of each chapter., 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., 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., This text is 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 modeling. Mathematical definitions, theorems, proofs, and a number of classroom examples help the student to fully grasp the content of the main results, and problems of varying difficulty are proposed at the end of each chapter. The material is accessible to students who know the basics of probability theory, but a review of probability is included to make the text largely self-contained. It brings students to the borders of current research covering more advanced topics such as Martingales, eigenvalue, Gibbs fields and Monte Carlo techniques.
LC Classification NumberQA273.A1-274.9
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