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Two-type linear-fractional branching processes in varying environments with asymptotically constant mean matrices
Published online by Cambridge University Press: 07 February 2022
Abstract
Consider two-type linear-fractional branching processes in varying environments with asymptotically constant mean matrices. Let
$\nu$
be the extinction time. Under certain conditions, we show that both
$\mathbb{P}(\nu=n)$
and
$\mathbb{P}(\nu>n)$
are asymptotically the same as some functions of the products of spectral radii of the mean matrices. We also give an example for which
$\mathbb{P}(\nu=n)$
decays with various speeds such as
${c}/({n^{1/2}\log n)^2}$
,
${c}/{n^\beta}$
,
$\beta >1$
, which are very different from those of homogeneous multitype Galton–Watson processes.
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- Copyright
- © The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust
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