Quasi-Stationary Distributions of Reversible Ergodic Markov Chains Without Absorbing States

The authors introduce a new notion of quasi-stationary distribution for reversible ergodic Markov chains without absorbing states. This generalization of the classical quasi-stationary distribution is characterized by an optimal strong stationary time, representing the "hitting time of the stationary distribution", and exhibits similar exponential behavior and geometric interpretation as the classical case.