LEADER 04209nam 22006975 450 001 9910808755403321 005 20240516013802.0 010 $a1-4757-3124-8 024 7 $a10.1007/978-1-4757-3124-8 035 $a(CKB)2660000000022230 035 $a(SSID)ssj0001297489 035 $a(PQKBManifestationID)11775306 035 $a(PQKBTitleCode)TC0001297489 035 $a(PQKBWorkID)11367557 035 $a(PQKB)10449291 035 $a(DE-He213)978-1-4757-3124-8 035 $a(MiAaPQ)EBC3087178 035 $a(PPN)238044076 035 $a(EXLCZ)992660000000022230 100 $a20130107d1999 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aMarkov Chains $eGibbs Fields, Monte Carlo Simulation, and Queues /$fby Pierre Bremaud 205 $a1st ed. 1999. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1999. 215 $a1 online resource (XVIII, 445 p. 3 illus.) 225 1 $aTexts in Applied Mathematics,$x0939-2475 ;$v31 300 $a"With 64 Illustrations." 311 $a0-387-98509-3 311 $a1-4419-3131-7 320 $aIncludes bibliographical references and indexes. 327 $a1 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. 330 $aIn this book, the author begins with the elementary theory of Markov chains and very progressively brings the reader to the more advanced topics. He gives a useful review of probability that makes the book self-contained, and provides an appendix with detailed proofs of all the prerequisites from calculus, algebra, and number theory. A number of carefully chosen problems of varying difficulty are proposed at the close of each chapter, and the mathematics are slowly and carefully developed, in order to make self-study easier. The author treats the classic topics of Markov chain theory, both in discrete time and continuous time, as well as the connected topics such as finite Gibbs fields, nonhomogeneous Markov chains, discrete- time regenerative processes, Monte Carlo simulation, simulated annealing, and queuing theory. The result is an up-to-date textbook on stochastic processes. Students and researchers in operations research and electrical engineering, as well as in physics and biology, will find it very accessible and relevant. 410 0$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 $a519.2 676 $a519.233 700 $aBremaud$b Pierre$4aut$4http://id.loc.gov/vocabulary/relators/aut$056619 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910808755403321 996 $aMarkov chains$9735551 997 $aUNINA