On Times to Quasi-stationarity for Birth and Death Processes

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The Passage Time Distribution for a Birth-and-Death Chain: Strong Stationary Duality Gives a First Stochastic Proof (2007, methodology): “A well-known theorem usually attributed to Keilson [12] (Theorem 5.1A, together with Remark 5.1B; see also Section 1 of [11]), but which—as pointed out by Laurent SaloffCoste via Diaconis and Miclo [5]—can be traced back at least as far as Karlin and McGregor [10, equation (45)], states that, for an”
On Hitting Times and Fastest Strong Stationary Times for Skip-Free and More General Chains (2007, background): “Diaconis and Miclo recently obtained the first such representation, but our construction is much simpler.”