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We characterize absorption-time distributions for birth-death Markov chainswith an absorbing boundary. For "extinction-prone" chains (which drift onaverage toward the absorbing state) the asymptotic distribution is Gaussian,Gumbel, or belongs to a family of skewed distributions. The latter two casesarise when the dynamics slow down dramatically near the boundary. Severalmodels of evolution, epidemics, and chemical reactions fall into these classes;in each case we establish new results for the absorption-time distribution.Applications to African sleeping sickness are discussed.

Asymptotic absorption-time distributions in extinction-prone Markov processes