LEADER 05581nam 2200757 450 001 9910141723003321 005 20200520144314.0 010 $a1-118-88187-7 010 $a1-118-88186-9 010 $a1-118-88269-5 035 $a(CKB)2560000000148628 035 $a(EBL)1666496 035 $a(SSID)ssj0001181611 035 $a(PQKBManifestationID)11639745 035 $a(PQKBTitleCode)TC0001181611 035 $a(PQKBWorkID)11144219 035 $a(PQKB)11032514 035 $a(OCoLC)880451357 035 $a(DLC) 2013050092 035 $a(Au-PeEL)EBL1666496 035 $a(CaPaEBR)ebr10862687 035 $a(CaONFJC)MIL599742 035 $a(OCoLC)877769913 035 $a(CaSebORM)9781118882696 035 $a(MiAaPQ)EBC1666496 035 $a(PPN)18391032X 035 $a(EXLCZ)992560000000148628 100 $a20140502h20142014 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMarkov chains $eanalytic and Monte Carlo computations /$fCarl Graham 205 $aFirst edition. 210 1$aWest Sussex, England :$cJohn Wiley & Sons,$d2014. 210 4$dİ2014 215 $a1 online resource (260 p.) 225 1 $aWiley Series in Probability and Statistics 300 $aDescription based upon print version of record. 311 $a1-306-68491-9 311 $a1-118-51707-5 320 $aIncludes bibliographical references and index. 327 $aCover; Title Page; Copyright; Contents; Preface; List of Figures; Nomenclature; Introduction; Chapter 1 First steps; 1.1 Preliminaries; 1.2 First properties of Markov chains; 1.2.1 Markov chains, finite-dimensional marginals, and laws; 1.2.2 Transition matrix action and matrix notation; 1.2.3 Random recursion and simulation; 1.2.4 Recursion for the instantaneous laws, invariant laws; 1.3 Natural duality: algebraic approach; 1.3.1 Complex eigenvalues and spectrum; 1.3.2 Doeblin condition and strong irreducibility; 1.3.3 Finite state space Markov chains; 1.4 Detailed examples 327 $a1.4.1 Random walk on a network1.4.2 Gambler's ruin; 1.4.3 Branching process: evolution of a population; 1.4.4 Ehrenfest's Urn; 1.4.5 Renewal process; 1.4.6 Word search in a character chain; 1.4.7 Product chain; Exercises; Chapter 2 Past, present, and future; 2.1 Markov property and its extensions; 2.1.1 Past ?-field, filtration, and translation operators; 2.1.2 Markov property; 2.1.3 Stopping times and strong Markov property; 2.2 Hitting times and distribution; 2.2.1 Hitting times, induced chain, and hitting distribution; 2.2.2 ""One step forward'' method, Dirichlet problem 327 $a2.3 Detailed examples2.3.1 Gambler's ruin; 2.3.2 Unilateral hitting time for a random walk; 2.3.3 Exit time from a box; 2.3.4 Branching process; 2.3.5 Word search; Exercises; Chapter 3 Transience and recurrence; 3.1 Sample paths and state space; 3.1.1 Communication and closed irreducible classes; 3.1.2 Transience and recurrence, recurrent class decomposition; 3.1.3 Detailed examples; 3.2 Invariant measures and recurrence; 3.2.1 Invariant laws and measures; 3.2.2 Canonical invariant measure; 3.2.3 Positive recurrence, invariant law criterion; 3.2.4 Detailed examples; 3.3 Complements 327 $a3.3.1 Hitting times and superharmonic functions3.3.2 Lyapunov functions; 3.3.3 Time reversal, reversibility, and adjoint chain; 3.3.4 Birth-and-death chains; Exercises; Chapter 4 Long-time behavior; 4.1 Path regeneration and convergence; 4.1.1 Pointwise ergodic theorem, extensions; 4.1.2 Central limit theorem for Markov chains; 4.1.3 Detailed examples; 4.2 Long-time behavior of the instantaneous laws; 4.2.1 Period and aperiodic classes; 4.2.2 Coupling of Markov chains and convergence in law; 4.2.3 Detailed examples; 4.3 Elements on the rate of convergence for laws 327 $a4.3.1 The Hilbert space framework4.3.2 Dirichlet form, spectral gap, and exponential bounds; 4.3.3 Spectral theory for reversible matrices; 4.3.4 Continuous-time Markov chains; Exercises; Chapter 5 Monte Carlo methods; 5.1 Approximate solution of the Dirichlet problem; 5.1.1 General principles; 5.1.2 Heat equation in equilibrium; 5.1.3 Heat equation out of equilibrium; 5.1.4 Parabolic partial differential equations; 5.2 Invariant law simulation; 5.2.1 Monte Carlo methods and ergodic theorems; 5.2.2 Metropolis algorithm, Gibbs law, and simulated annealing 327 $a5.2.3 Exact simulation and backward recursion 330 $a Markov Chains: Analytic and Monte Carlo Computations introduces the main notions related to Markov chains and provides explanations on how to characterize, simulate, and recognize them. Starting with basic notions, this book leads progressively to advanced and recent topics in the field, allowing the reader to master the main aspects of the classical theory. This book also features: Numerous exercises with solutions as well as extended case studies.A detailed and rigorous presentation of Markov chains with discrete time and state space.An appendix present 410 0$aWiley series in probability and statistics. 606 $aMarkov processes 606 $aMonte Carlo method 606 $aNumerical calculations 615 0$aMarkov processes. 615 0$aMonte Carlo method. 615 0$aNumerical calculations. 676 $a519.2/33 700 $aGraham$b C$g(Carl),$0349837 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910141723003321 996 $aMarkov chains$91969499 997 $aUNINA