LEADER 04457nam 22006375 450 001 9910483245103321 005 20211005213533.0 010 $a3-030-45982-9 024 7 $a10.1007/978-3-030-45982-6 035 $a(CKB)4100000011273708 035 $a(MiAaPQ)EBC6208759 035 $a(DE-He213)978-3-030-45982-6 035 $a(MiAaPQ)EBC6420099 035 $a(Au-PeEL)EBL6420099 035 $a(OCoLC)1156238633 035 $a(PPN)248395041 035 $a(EXLCZ)994100000011273708 100 $a20200523d2020 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMarkov Chains $eGibbs Fields, Monte Carlo Simulation and Queues /$fby Pierre Brémaud 205 $a2nd ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (564 pages) 225 1 $aTexts in Applied Mathematics,$x0939-2475 ;$v31 311 $a3-030-45981-0 320 $aIncludes bibliographical references and index. 327 $aPreface -- 1 Probability Review -- 2 Discrete-Time Markov Chains -- 3 Recurrence and Ergodicity -- 4 Long-Run Behavior -- 5 Discrete-Time Renewal Theory -- 6 Absorption and Passage Times -- 7 Lyapunov Functions and Martingales -- 8 Random Walks on Graphs -- 9 Convergence Rates -- 10 Markov Fields on Graphs -- 11 Monte Carlo Markov Chains -- 12 Non-homogeneous Markov Chains -- 13 Continuous-Time Markov Chains -- 14 Markovian Queueing Theory -- Appendices -- Bibliography -- Index. 330 $aThis 2nd edition is a thoroughly revised and augmented version of the book with the same title published in 1999. The author begins with the elementary theory of Markov chains and very progressively brings the reader to more advanced topics. He gives a useful review of probability, making the book self-contained, and provides an appendix with detailed proofs of all the prerequisites from calculus, algebra, and number theory. A number of carefully chosen problems of varying difficulty are proposed at the close of each chapter, and the mathematics is slowly and carefully developed, in order to make self-study easier. The book treats the classical topics of Markov chain theory, both in discrete time and continuous time, as well as connected topics such as finite Gibbs fields, nonhomogeneous Markov chains, discrete-time regenerative processes, Monte Carlo simulation, simulated annealing, and queuing theory. The main additions of the 2nd edition are the exact sampling algorithm of Propp and Wilson, the electrical network analogy of symmetric random walks on graphs, mixing times and additional details on the branching process. The structure of the book has been modified in order to smoothly incorporate this new material. Among the features that should improve reader-friendliness, the three main ones are: a shared numbering system for the definitions, theorems and examples; the attribution of titles to the examples and exercises; and the blue highlighting of important terms. The result is an up-to-date textbook on stochastic processes. Students and researchers in operations research and electrical engineering, as well as in physics and biology, will find it very accessible and relevant. 410 0$aTexts in Applied Mathematics,$x0939-2475 ;$v31 606 $aProbabilities 606 $aOperations research 606 $aDecision making 606 $aElectrical engineering 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aOperations Research/Decision Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/521000 606 $aElectrical Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T24000 615 0$aProbabilities. 615 0$aOperations research. 615 0$aDecision making. 615 0$aElectrical engineering. 615 14$aProbability Theory and Stochastic Processes. 615 24$aOperations Research/Decision Theory. 615 24$aElectrical Engineering. 676 $a519.233 700 $aBrémaud$b Pierre$4aut$4http://id.loc.gov/vocabulary/relators/aut$056619 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483245103321 996 $aMarkov chains$9735551 997 $aUNINA