First hitting and strong metastability times

F. Manzo; E. Scoppola

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arXiv · 1807.11574

First hitting and strong metastability times

F. Manzo·E. Scoppola

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Abstract

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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BibTeX RIS

F. Manzo, E. Scoppola. 2018-07-17. First hitting and strong metastability times. https://arxiv.org/abs/1807.11574

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