03805nam a22005415i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001900153050001600172072001600188072001700204072002300221082001400244100002900258245013600287250002000423264006700443300003500510336002600545337002600571338003600597347002400633490006700657505057500724520133401299650001702633650002802650650002502678650002402703650001902727650002502746650002902771650001702800650004902817650006202866650004502928650005902973700002603032710003403058773002003092776003603112830006703148856004803215978-1-4614-4346-9DE-He21320180115171521.0cr nn 008mamaa121116s2013 xxu| s |||| 0|eng d a97814614434697 a10.1007/978-1-4614-4346-92doi 4aQA273.A1-274.9 4aQA274-274.9 7aPBT2bicssc 7aPBWL2bicssc 7aMAT0290002bisacsh04a519.22231 aYin, G. George.eauthor.10aContinuous-Time Markov Chains and Applicationsh[electronic resource] :bA Two-Time-Scale Approach /cby G. George Yin, Qing Zhang. aSecond edition. 1aNew York, NY :bSpringer New York :bImprint: Springer,c2013. aXXII, 430 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aStochastic Modelling and Applied Probability,x0172-4568 ;v370 aPrologue and Preliminaries: Introduction and overview- Mathematical preliminaries -- Markovian models -- Two-Time-Scale Markov Chains: Asymptotic Expansions of Solutions for Forward Equations -- Occupation Measures: Asymptotic Properties and Ramification -- Asymptotic Expansions of Solutions for Backward Equations -- Applications:MDPs, Near-optimal Controls, Numerical Methods, and LQG with Switching: Markov Decision Problems -- Stochastic Control of Dynamical Systems -- Numerical Methods for Control and Optimization -- Hybrid LQG Problems -- References -- Index.-. aThis book gives a systematic treatment of singularly perturbed systems that naturally arise in control and optimization, queueing networks, manufacturing systems, and financial engineering. It presents results on asymptotic expansions of solutions of Komogorov forward and backward equations, properties of functional occupation measures, exponential upper bounds, and functional limit results for Markov chains with weak and strong interactions. To bridge the gap between theory and applications, a large portion of the book is devoted to applications in controlled dynamic systems, production planning, and numerical methods for controlled Markovian systems with large-scale and complex structures in the real-world problems. This second edition has been updated throughout and includes two new chapters on asymptotic expansions of solutions for backward equations and hybrid LQG problems. The chapters on analytic and probabilistic properties of two-time-scale Markov chains have been almost completely rewritten and the notation has been streamlined and simplified. This book is written for applied mathematicians, engineers, operations researchers, and applied scientists. Selected material from the book can also be used for a one semester advanced graduate-level course in applied probability and stochastic processes. 0aMathematics. 0aCalculus of variations. 0aOperations research. 0aManagement science. 0aProbabilities. 0aApplied mathematics. 0aEngineering mathematics.14aMathematics.24aProbability Theory and Stochastic Processes.24aCalculus of Variations and Optimal Control; Optimization.24aOperations Research, Management Science.24aAppl.Mathematics/Computational Methods of Engineering.1 aZhang, Qing.eauthor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9781461443452 0aStochastic Modelling and Applied Probability,x0172-4568 ;v3740uhttp://dx.doi.org/10.1007/978-1-4614-4346-9