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A note on the asymptotic behaviour of the extinction probability in supercritical population-size-dependent branching processes with independent and identically distributed random environments
Published online by Cambridge University Press: 14 July 2016
Abstract
In supercritical population-size-dependent branching processes with independent and identically distributed random environments, it is shown that under certain regularity conditions there exist constants 0 < α 1 ≤α 0 < + ∞ and 0 < C 1, C 2 < + ∞ such that the extinction probability starting with k individuals is bounded below by C 1 k -α 0 and above by C 2 k -α 1 for sufficiently large k. Moreover, a similar conclusion, which follows from a result of Höpfner, is presented along with some remarks.
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- Copyright © Applied Probability Trust 2004
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