Transcription of 4 Absorbing Markov Chains - SSCC - Home
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Last revised: 8 February 20094 Absorbing Markov ChainsSo far, we have focused onregularMarkov Chains for which the transition matrixPis primitive. Because primitivity requiresP(i, i)<1 for every statei, regular chainsnever get stuck in a particular state. However, other Markov Chains may have oneor moreabsorbing states. By definition, stateiis Absorbing whenP(i, i) = 1 (andhenceP(i, j) = 0 for allj6=i). In turn, the chain itself is called anabsorbing chainwhen it satisfies two conditions. First, the chain has at least one Absorbing , it is possible to transition from each non- Absorbing state to some absorbingstate (perhaps in multiple steps).
4 Absorbing Markov Chains So far, we have focused on regular Markov chains for which the transition matrix P is primitive. Because primitivity requires P(i,i) < 1 for every state i, regular chains never get “stuck” in a particular state. However, other Markov chains may have one
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