In the setting of non-reversible Markov chains on finite or countable state space, exact results on the distribution of the first hitting time to a given set $G$ are obtained. A new notion of strong metastability time is introduced to describe the local relaxation time. This time is defined via a generalization of the strong stationary time to a conditionally strong quasi-stationary time(CSQST). Rarity of the target set $G$ is not required and the initial distribution can be completely general. The results clarify the the role played by the initial distribution on the exponential law; they are used to give a general notion of metastability and to discuss the relation between the exponential distribution of the first hitting time and metastability.
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