  Keeping in view applications to numerical simulations of the evolution of a
nuclear reactor core around criticality, we use a general mathematical
framework for describing the evolutions of multiplicative processes (processes
involving particle creation) both in particle generations and in time. This
framework allows us to obtain, within a same formalism, two corresponding
estimates of the multiplication factor which describes the growth of particle
numbers at large times. We obtain the relative positions of both estimates with
respect to each other and to criticality. These relations may show particularly
useful when simulating in a realistic way the monitoring of nuclear cores in
subcritical states, such as is the case for Accelerator Driven Systems (ADS).
More generally, this study applies to various multiplicative processes which
can be found in nature.
