Asymptotic Absorption-Time Distributions in Extinction-Prone Markov Processes
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.
- Publication:
-
Physical Review Letters
- Pub Date:
- May 2022
- DOI:
- 10.1103/PhysRevLett.128.218301
- arXiv:
- arXiv:2103.08522
- Bibcode:
- 2022PhRvL.128u8301H
- Keywords:
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- Condensed Matter - Statistical Mechanics;
- Quantitative Biology - Populations and Evolution
- E-Print:
- 6 pages, 4 figures, 11 page supplemental material