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Семинар отдела дискретной математики МИАН
7 декабря 2021 г. 16:00, г. Москва, МИАН, комн. 511 (ул. Губкина, 8)
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Critical branching as a pure death process coming down from infinity
S. M. Sagitov Department of Mathematical Sciences, Chalmers University of Technology and the University of Göteborg
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Аннотация:
We consider the critical Galton-Watson process with overlapping generations stemming from a single founder. Assuming that both the variance of the offspring number and the average generation length are finite, we establish the convergence of the finite-dimensional distributions, conditioned on non-extinction at a remote time of observation. The limiting process is identified as a pure death process coming down from infinity.
This result brings a new perspective on Vatutin's dichotomy claiming that in the critical regime of age-dependent reproduction, an extant population either contains a large number of short-living individuals or consists of few long-living individuals.
Язык доклада: английский
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