Asymptotic absorption-time distributions in extinction-prone Markov processes

TL;DR

This paper analyzes the distribution of absorption times in birth-death Markov chains that tend toward extinction, revealing Gaussian, Gumbel, or skewed distributions depending on the dynamics near the boundary.

Contribution

It provides a comprehensive characterization of asymptotic absorption-time distributions for extinction-prone Markov processes, including new results for various models.

Findings

Absorption times are Gaussian, Gumbel, or skewed distributions.

Dynamics slow down near the boundary, affecting the distribution shape.

Applications include models of evolution, epidemics, and chemical reactions.

Abstract

We characterize absorption-time distributions for birth-death Markov chains with an absorbing boundary. For "extinction-prone" chains (which drift on average toward the absorbing state) the asymptotic distribution is Gaussian, Gumbel, or belongs to a family of skewed distributions. The latter two cases arise when the dynamics slow down dramatically near the boundary. Several models 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.