03694nam 22007215 450 991043803700332120250317122252.09789814451512981445151710.1007/978-981-4451-51-2(CKB)3710000000015997(EBL)1398361(SSID)ssj0000988317(PQKBManifestationID)11627773(PQKBTitleCode)TC0000988317(PQKBWorkID)10952218(PQKB)10075198(DE-He213)978-981-4451-51-2(MiAaPQ)EBC6312731(MiAaPQ)EBC1398361(Au-PeEL)EBL1398361(CaPaEBR)ebr10976331(OCoLC)857281878(PPN)172434734(EXLCZ)99371000000001599720130807d2013 u| 0engur|n|---|||||txtccrUnderstanding Markov Chains Examples and Applications /by Nicolas Privault1st ed. 2013.Singapore :Springer Nature Singapore :Imprint: Springer,2013.1 online resource (357 p.)Springer Undergraduate Mathematics Series,2197-4144Description based upon print version of record.9789814451505 9814451509 Introduction -- 1) Probability Background -- 2) Gambling Problems -- 3) Random Walks -- 4) Discrete-Time Markov Chains -- 5) First Step Analysis -- 6) Classication of States -- 7) Long-Run Behavior of Markov Chains -- 8) Branching Processes -- 9) Continuous-Time Markov Chains -- 10) Discrete-Time Martingales -- 11) Spatial Poisson Processes -- 12) Reliability Theory -- Some Useful Identities -- Solutions to the Exercises -- References -- Index.This book provides an undergraduate introduction to discrete and continuous-time Markov chains and their applications. A large focus is placed on the first step analysis technique and its applications to average hitting times and ruin probabilities. Classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes, are also covered. Two major examples (gambling processes and random walks) are treated in detail from the beginning, before the general theory itself is presented in the subsequent chapters. An introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times is also provided, and the book includes a chapter on spatial Poisson processes with some recent results on moment identities and deviation inequalities for Poisson stochastic integrals. The concepts presented are illustrated by examples and by 72 exercises and their complete solutions.Springer Undergraduate Mathematics Series,2197-4144ProbabilitiesStatisticsStatisticsProbability TheoryStatistical Theory and MethodsStatistics in Engineering, Physics, Computer Science, Chemistry and Earth SciencesProbabilities.Statistics.Statistics.Probability Theory.Statistical Theory and Methods.Statistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences.519.233Privault Nicolasauthttp://id.loc.gov/vocabulary/relators/aut475313MiAaPQMiAaPQMiAaPQBOOK9910438037003321Understanding Markov Chains1563914UNINA