LEADER 03861nam 22006735 450 001 9910438037003321 005 20200703022611.0 010 $a981-4451-51-7 024 7 $a10.1007/978-981-4451-51-2 035 $a(CKB)3710000000015997 035 $a(EBL)1398361 035 $a(SSID)ssj0000988317 035 $a(PQKBManifestationID)11627773 035 $a(PQKBTitleCode)TC0000988317 035 $a(PQKBWorkID)10952218 035 $a(PQKB)10075198 035 $a(DE-He213)978-981-4451-51-2 035 $a(MiAaPQ)EBC6312731 035 $a(MiAaPQ)EBC1398361 035 $a(Au-PeEL)EBL1398361 035 $a(CaPaEBR)ebr10976331 035 $a(OCoLC)857281878 035 $a(PPN)172434734 035 $a(EXLCZ)993710000000015997 100 $a20130807d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aUnderstanding Markov Chains $eExamples and Applications /$fby Nicolas Privault 205 $a1st ed. 2013. 210 1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2013. 215 $a1 online resource (357 p.) 225 1 $aSpringer Undergraduate Mathematics Series,$x1615-2085 300 $aDescription based upon print version of record. 311 $a981-4451-50-9 327 $aIntroduction -- 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. 330 $aThis book provides an undergraduate introduction to discrete and continuous-time Markov chains and their applications. A large focus is placed on the first step analysis technique and its applications to average hitting times and ruin probabilities. Classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes, are also covered. Two major examples (gambling processes and random walks) are treated in detail from the beginning, before the general theory itself is presented in the subsequent chapters. An introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times is also provided, and the book includes a chapter on spatial Poisson processes with some recent results on moment identities and deviation inequalities for Poisson stochastic integrals. The concepts presented are illustrated by examples and by 72 exercises and their complete solutions. 410 0$aSpringer Undergraduate Mathematics Series,$x1615-2085 606 $aProbabilities 606 $aStatistics  606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aStatistical Theory and Methods$3https://scigraph.springernature.com/ontologies/product-market-codes/S11001 606 $aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/S17020 615 0$aProbabilities. 615 0$aStatistics . 615 14$aProbability Theory and Stochastic Processes. 615 24$aStatistical Theory and Methods. 615 24$aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. 676 $a519.233 700 $aPrivault$b Nicolas$4aut$4http://id.loc.gov/vocabulary/relators/aut$0475313 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438037003321 996 $aUnderstanding Markov Chains$91563914 997 $aUNINA