The elapsed time between two transient state observations for an absorbing Markov chain

2015/11/03 by Bianca De Sanctis, De Sanctis, Bianca, A. P. Jason de Koning +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #60J10 #Evolution and Genetic Dynamics #FOS: Biological sciences #FOS: Mathematics #Gene Regulatory Network Analysis #Genetic Mapping and Diversity in Plants and Animals #Genetics, Aging, and Longevity in Model Organisms #Populations and Evolution (q-bio.PE) #Probability (math.PR) #math.PR #msc:60J10 #q-bio.PE

paper · pdf · doi:10.48550/arxiv.1511.01067

11 pages

arxiv created 2015/11/03 · openalex publication_date 2015/11/03 · arxiv updated 2015/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider a system evolving according to an absorbing discrete-time Markov chain with known transition matrix. The state of the system is observed at two points in time, separated by an unknown number of generations. We are interested in calculating the expected elapsed time and its variance. We provide a novel, exact solution, which is computable from the fundamental matrix of a related absorbing Markov chain. This solution may be useful in population genetics for computing the expected age of a segregating allele without requiring diffusion approximation.

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