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CHAPTER IIBASIC CONCEPTS OF MARKOV CHAINS
CHAPTER IIIABSORBING MARKOV CHAINS
CHAPTER IVREGULAR MARKOV CHAINS
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absorbing chain absorption application assigned assume called Chapter components compute condition consider corresponding cyclic defined DEFINITION denoted depend determined elements entered entries equal equivalence class ergodic chain ergodic set example Exercise expanded expect experiment fact finite fixed vector function fundamental matrix given gives Hence independent industry initial interesting interpretation limiting lumpability lumped Markov chain mean number measure method moves observed obtain original chain outcome partition passage path positive possible probability vector PROOF prove quantities questions random walk reach regular relation respect reverse satisfied sequence simple single stage starting statement steps subset sufficient symmetric matrix tends THEOREM theory transient transition matrix tree true truth weights