LEADER 03067nam 22005895 450 001 9910300101903321 005 20250317122253.0 010 $a9789811306594 010 $a9811306591 024 7 $a10.1007/978-981-13-0659-4 035 $a(CKB)4100000005472070 035 $a(DE-He213)978-981-13-0659-4 035 $a(MiAaPQ)EBC6315174 035 $a(PPN)229916759 035 $a(EXLCZ)994100000005472070 100 $a20180803d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aUnderstanding Markov Chains $eExamples and Applications /$fby Nicolas Privault 205 $a2nd ed. 2018. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2018. 215 $a1 online resource (XVII, 372 p. 44 illus.) 225 1 $aSpringer Undergraduate Mathematics Series,$x2197-4144 311 08$a9789811306587 311 08$a9811306583 327 $aProbability Background -- Gambling Problems -- Random Walks -- Discrete-Time Markov Chains -- First Step Analysis -- Classification of States -- Long-Run Behavior of Markov Chains -- Branching Processes -- Continuous-Time Markov Chains -- Discrete-Time Martingales -- Spatial Poisson Processes -- Reliability Theory. 330 $aThis book provides an undergraduate-level introduction to discrete and continuous-time Markov chains and their applications, with a particular focus on the first step analysis technique and its applications to average hitting times and ruin probabilities. It also discusses classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes. It first examines in detail two important examples (gambling processes and random walks) before presenting the general theory itself in the subsequent chapters. It also provides an introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times, together with a chapter on spatial Poisson processes. The concepts presented are illustrated by examples, 138 exercises and 9 problems with their solutions. 410 0$aSpringer Undergraduate Mathematics Series,$x2197-4144 606 $aProbabilities 606 $aStatistics 606 $aStatistics 606 $aProbability Theory 606 $aStatistical Theory and Methods 606 $aStatistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences 615 0$aProbabilities. 615 0$aStatistics. 615 0$aStatistics. 615 14$aProbability Theory. 615 24$aStatistical Theory and Methods. 615 24$aStatistics in 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 $a9910300101903321 996 $aUnderstanding Markov Chains$91563914 997 $aUNINA