MARC Record from marc_columbia

LEADER: 04080cam a2200649M 4500
001 16273057
005 20220703225710.0
006 m o d
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035 $a(OCoLC)ocn964333653
035 $a(NNC)16273057
040 $aYDX$beng$epn$cYDX$dOCLCQ$dN$T$dOCLCF$dSTF$dOCLCQ$dOCLCO
019 $a982149676$a982230612
020 $a3037195711$q(electronic bk.)
020 $a9783037195710$q(electronic bk.)
024 70 $a10.4171/071$2doi
035 $a(OCoLC)964333653$z(OCoLC)982149676$z(OCoLC)982230612
050 4 $aQA274.7
072 7 $aMAT$x003000$2bisacsh
072 7 $aMAT$x029000$2bisacsh
072 7 $aPBT$2bicssc
082 04 $a519.233$222
084 $a60-xx$2msc
049 $aZCUA
100 1 $aWOLFGANG WOESS.
245 10 $aDENUMERABLE MARKOV CHAINS;GENERATING FUNCTIONS, BOUNDARY THEORY, RANDOM WALKS ON TREES.
260 $a[Place of publication not identified] :$bEUROPEAN MATHEMATICAL SOC.
300 $a1 online resource.
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
347 $atext file$bPDF$2rda
490 0 $aEMS Textbooks in Mathematics (ETB)
520 $aMarkov chains are the first and most important examples of random processes. This book is about time-homogeneous Markov chains that evolve with discrete time steps on a countable state space. Measure theory is not avoided, careful and complete proofs are provided. A specific feature is the systematic use, on a relatively elementary level, of generating functions associated with transition probabilities for analyzing Markov chains. Basic definitions and facts include the construction of the trajectory space and are followed by ample material concerning recurrence and transience, the convergence and ergodic theorems for positive recurrent chains. There is a side-trip to the Perron-Frobenius theorem. Special attention is given to reversible Markov chains and to basic mathematical models of "population evolution" such as birth-and-death chains, Galton-Watson process and branching Markov chains. A good part of the second half is devoted to the introduction of the basic language and elements of the potential theory of transient Markov chains. Here the construction and properties of the Martin boundary for describing positive harmonic functions are crucial. In the long final chapter on nearest neighbour random walks on (typically infinite) trees the reader can harvest from the seed of methods laid out so far, in order to obtain a rather detailed understanding of a specific, broad class of Markov chains. The level varies from basic to more advanced, addressing an audience from master's degree students to researchers in mathematics, and persons who want to teach the subject on a medium or advanced level. A specific characteristic of the book is the rich source of classroom-tested exercises with solutions.
650 0 $aMarkov processes.
650 0 $aGenerating functions.
650 0 $aRandom walks (Mathematics)
650 0 $aBoundary value problems.
650 0 $aMeasure theory.
650 6 $aProcessus de Markov.
650 6 $aFonctions génératrices.
650 6 $aMarches aléatoires (Mathématiques)
650 6 $aProblèmes aux limites.
650 6 $aThéorie de la mesure.
650 07 $aProbability & statistics.$2bicssc
650 7 $aMATHEMATICS$xApplied.$2bisacsh
650 7 $aMATHEMATICS$xProbability & Statistics$xGeneral.$2bisacsh
650 7 $aBoundary value problems.$2fast$0(OCoLC)fst00837122
650 7 $aGenerating functions.$2fast$0(OCoLC)fst00939866
650 7 $aMarkov processes.$2fast$0(OCoLC)fst01010347
650 7 $aMeasure theory.$2fast$0(OCoLC)fst01013175
650 7 $aRandom walks (Mathematics)$2fast$0(OCoLC)fst01089818
650 07 $aProbability theory and stochastic processes.$2msc
655 4 $aElectronic books.
856 40 $uhttp://www.columbia.edu/cgi-bin/cul/resolve?clio16273057$zAll EBSCO eBooks
852 8 $blweb$hEBOOKS