Considering one finite state discrete Markov chain and there are multiple transient states and multiple absorbing states. If there is a set of transient states A and the specific state i belongs to set A. My questions are, is there any algorithm can give us the information of how many times it will cross (in and out) this set if we begin with state i before absorption? is there any algorithm can give us the information of how many times it will cross this set before it is absorbed by one specific absorbing state?
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The answer is 1. If you start in the set of transient states, once you leave that set then you can never return. – Michael Jun 11 '21 at 15:40
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If I replace transient states by non-absorbing states, is there any difference? – Wang Simon Jun 11 '21 at 15:57
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I assume you want to find mean time in transient states (in set A) before getting absorbed? There should be a formula for that, look up "mean time in transient states" – Cat Mai Jun 24 '21 at 00:55
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Nope I just want to know that if there is a partitioned of state space and I want to know that how many times we can visit on subsets of state space before absorption and I found that some very useful theory of dependability for Systems with a partitioned state space but that book just give us the probability generating function of visit times and I don’t know the mean of this visit times and I just want some help here. – Wang Simon Jun 27 '21 at 11:00