  In the present paper, we focus on semi-parametric methods for estimating the
absorption probability and the distribution of the absorbing time of a
growth-fragmentation model observed within a long time interval. We establish
that the absorption probability is the unique solution in an appropriate space
of a Fredholm equation of the second kind whose parameters are unknown. We
estimate this important characteristic of the underlying process by solving
numerically the estimated Fredholm equation. Even if the study has been
conducted for a particular model, our method is quite general.
