Given a continuous Markov chains (and given the transition rates between the states) I would like to know the following:
- mean time of permanence for all states.
- higher order moments (i.e., variance and, possibly, CDF?)
In particular, I am also interested about computing the above quantities in the case when the system has to stay at least for a fixed amount of time in every state. For example, suppose there are for states {A, B, C, D}. When the system is in state A, it has to stay there for at least $T_A$ seconds, and the same for state B ($T_B$ seconds) and so on for all remaining states. In this case, is it still possible to determine the quantities in the list above, namely, mean permanence time for all states, variance and CDF?