  Understanding how galaxy properties are linked to the dark matter halos they
reside in, and how they co-evolve is a powerful tool to constrain the processes
related to galaxy formation. The stellar-to-halo mass relation (SHMR) and its
evolution over the history of the Universe provides insights on galaxy
formation models and allows to assign galaxy masses to halos in N-body dark
matter simulations. We use a statistical approach to link the observed galaxy
stellar mass functions on the COSMOS field to dark matter halo mass functions
from the DUSTGRAIN simulation and from a theoretical parametrization from z=0
to z=4. We also propose an empirical model to describe the evolution of the
stellar-to-halo mass relation as a function of redshift. We calculate the
star-formation efficiency (SFE) of galaxies and compare results with previous
works and semi-analytical models.
