Monte Carlo simulations of the disc white dwarf population

In order to understand the dynamical and chemical evolution of our Galaxy i t is of fundamental importance to study the local neighbourhood. White dwar f stars are ideal candidates to probe the history of the solar neighbourhoo d, since these 'fossil' stars have very long evolutionary time-scales and, at the same time, their evolution is relatively well understood. In fact, t he white dwarf luminosity function has been used for this purpose by severa l authors. However, a long-standing problem arises from the relatively poor statistics of the samples, especially at low luminosities. In this paper w e assess the statistical reliability of the white dwarf luminosity function by using a Monte Carlo approach.