000 03158nam a22004935i 4500
001 978-981-4451-51-2
003 DE-He213
005 20140220082947.0
007 cr nn 008mamaa
008 130807s2013 si | s |||| 0|eng d
020 _a9789814451512
_9978-981-4451-51-2
024 7 _a10.1007/978-981-4451-51-2
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aPrivault, Nicolas.
_eauthor.
245 1 0 _aUnderstanding Markov Chains
_h[electronic resource] :
_bExamples and Applications /
_cby Nicolas Privault.
264 1 _aSingapore :
_bSpringer Singapore :
_bImprint: Springer,
_c2013.
300 _aIX, 354 p. 71 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Undergraduate Mathematics Series,
_x1615-2085
505 0 _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.
520 _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.
650 0 _aMathematics.
650 0 _aDistribution (Probability theory).
650 0 _aMathematical statistics.
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aStatistical Theory and Methods.
650 2 4 _aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9789814451505
830 0 _aSpringer Undergraduate Mathematics Series,
_x1615-2085
856 4 0 _uhttp://dx.doi.org/10.1007/978-981-4451-51-2
912 _aZDB-2-SMA
999 _c100172
_d100172