  Over the last decade, ingenuous developments in Monte Carlo methods have
enabled the unbiased estimation of adjoint-weighted reactor parameters
expressed as bilinear forms, such as kinetics parameters and sensitivity
coefficients. A prominent example is the Iterated Fission Probability method,
which relies on the simulation of the fission chains descending from an
ancestor neutron: the neutron population at an asymptotic fission generation
yields an estimate of the importance function (and hence of the adjoint
fundamental eigenmode) at the phase-space coordinates of the ancestor neutron.
In this paper we first establish rigorous results concerning the moments of the
asymptotic neutron population stemming from a single initial particle, with
special focus on the average and the variance. Then, we propose a simple
benchmark configuration where exact solutions are derived for these moments,
which can be used for the verification of new functionalities of production
Monte Carlo codes involving the Iterated Fission Probability method.
