Is there any approach to approximate the expected number of transitions to complete a Markov chain without knowing the exact transition probabilities? The reason I ask this is because I want to calculate the average number of events that can be modeled by some transitions in a Markov chain. The probabilities of transition are both very complicated to derive and the graph is very complecated. I don't need the exact model of the system though. Let me put the question this way: How can I simplify the Markov chain such that it can give a good approximation for the average number of required transitions to reach to a final state? It is no problem if it poorly models the system in any other sense.
Thanks!