%0 Journal Article
%T Harmonic continuous-time branching moments
%A Didier Piau
%J Mathematics
%D 2005
%I arXiv
%R 10.1214/105051606000000493
%X We 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.
%U http://arxiv.org/abs/math/0511058v2