02922nmm a2200337 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002000139245011200159250001700271260004800288300004300336505074600379653004801125653002401173653002701197653002701224653002001251653004001271653001801311710003401329041001901363989003801382490003301420856007201453082001001525520104901535EB000631342EBX0100000000000000048442400000000000000.0cr|||||||||||||||||||||140122 ||| eng a97814757312481 aBremaud, Pierre00aMarkov ChainshElektronische RessourcebGibbs Fields, Monte Carlo Simulation, and Queuescby Pierre Bremaud a1st ed. 1999 aNew York, NYbSpringer New Yorkc1999, 1999 aXVIII, 445 p. 3 illusbonline resource0 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 aProbability Theory and Stochastic Processes aOperations research aElectrical Engineering aElectrical engineering aDecision making aOperations Research/Decision Theory aProbabilities2 aSpringerLink (Online service)07aeng2ISO 639-2 bSBAaSpringer Book Archives -20040 aTexts in Applied Mathematics uhttps://doi.org/10.1007/978-1-4757-3124-8?nosfx=yxVerlag3Volltext0 a519.2 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