Dynamics of the time to the most recent common ancestor in a large branching population

DOI10.1214/09-AAP616zbMath1182.92054arXiv0812.1302OpenAlexW3104888206MaRDI QIDQ2268719

Steven N. Evans, Peter L. Ralph

Publication date: 8 March 2010

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0812.1302

zbMATH Keywords

Besseldualityrecurrencetransiencestationary distributionPoisson point processgenealogyself-similarmost recent common ancestorMRCApiecewise deterministiccontinuous state branchingPoisson cut-out

Mathematics Subject Classification ID

Problems related to evolution (92D15) Applications of branching processes (60J85) Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) (60J20) Self-similar stochastic processes (60G18) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (8)

Measure-valued continuous curves and processes in total variation norm ⋮ Tree-valued resampling dynamics martingale problems and applications ⋮ Local extinction in continuous-state branching processes with immigration ⋮ Smaller population size at the MRCA time for stationary branching processes ⋮ Time to most recent common ancestor for stationary continuous state branching processes with immigration ⋮ Time to the MRCA of a sample in a Wright-Fisher model with variable population size ⋮ Lamperti-type laws ⋮ Coalescences in continuous-state branching processes

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