  Rare trajectories of stochastic systems are important to understand --
because of their potential impact. However, their properties are by definition
difficult to sample directly. Population dynamics provides a numerical tool
allowing their study, by means of simulating a large number of copies of the
system, which are subjected to selection rules that favor the rare trajectories
of interest. Such algorithms are plagued by finite simulation time- and finite
population size- effects that can render their use delicate. In this paper, we
present a numerical approach which uses the finite-time and finite-size
scalings of estimators of the large deviation functions associated to the
distribution of rare trajectories. The method we propose allows one to extract
the infinite-time and infinite-size limit of these estimators which -- as shown
on the contact process -- provides a significant improvement of the large
deviation functions estimators compared to the the standard one.
