Harmonic continuous-time branching moments

dc.creatorPiau, Didier
dc.date2005-11-02
dc.date2007-02-14
dc.date.accessioned2026-07-07T07:46:37Z
dc.date.available2026-07-07T07:46:37Z
dc.descriptionWe show that the mean inverse populations of nondecreasing, square integrable, continuous-time branching processes decrease to zero like the inverse of their mean population if and only if the initial population $k$ is greater than a first threshold $m_1\ge1$. If, furthermore, $k$ is greater than a second threshold $m_2\ge m_1$, the normalized mean inverse population is at most $1/(k-m_2)$. We express $m_1$ and $m_2$ as explicit functionals of the reproducing distribution, we discuss some analogues for discrete time branching processes and link these results to the behavior of random products involving i.i.d. nonnegative sums.
dc.descriptionPublished at http://dx.doi.org/10.1214/105051606000000493 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0511058
dc.identifierhttp://arxiv.org/abs/math/0511058
dc.identifierAnnals of Applied Probability 2006, Vol. 16, No. 4, 2078-2097
dc.identifierdoi:10.1214/105051606000000493
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123888
dc.subjectProbability
dc.subject60J80 (Primary)
dc.titleHarmonic continuous-time branching moments
dc.typetext

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