We consider an individual which ultimately dies or divides, and whose state is subject to drift and jumps caused by external perturbations. The mortality and division rates being state-dependent, the present paper deals with the time-dependent distribution of the individual's position in the state-space and with its lifetime distribution. The results are applied to a model of a biological cell which is exposed to ionizing radiation. Under certain conditions on the parameters of the type of perturbation one can show that the division probability decreases and the mean regeneration time increases with increasing frequency and ‘effect' of the perturbations.
