We apply the empirical method built for redshift z = 0 in the previous work of Wang et al .
to a higher redshift , to link galaxy stellar mass directly with its hosting dark matter halo mass at redshift of around 0.8 .
The M _ { stars } - M _ { infall } relation of the galaxy stellar mass M _ { stars } and the host halo mass M _ { infall } is constrained by fitting both the stellar mass function and the correlation functions at different stellar mass intervals of the VVDS observation , where M _ { infall } is the mass of the hosting halo at the time when the galaxy was last the central galaxy .
We find that for low mass haloes , their residing central galaxies are less massive at high redshift than those at low redshift .
For high mass haloes , central galaxies in these haloes at high redshift are a bit more massive than the galaxies at low redshift .
Satellite galaxies are less massive at earlier times , for any given mass of hosting haloes .
Fitting both the SDSS and VVDS observations simultaneously , we also propose a unified model of the M _ { stars } - M _ { infall } relation , which describes the evolution of central galaxy mass as a function of time .
The stellar mass of a satellite galaxy is determined by the same M _ { stars } - M _ { infall } relation of central galaxies at the time when the galaxy is accreted and becomes a sub-component of a larger group .
With these models , we study the amount of galaxy stellar mass increased from z \sim 0.8 to the present day through galaxy mergers and star formation .
Low mass galaxies ( < 3 \times 10 ^ { 10 } h ^ { -1 } M _ { \odot } ) gain their stellar masses from z \sim 0.8 to z = 0 mainly through star formation .
For galaxies of higher mass , we find that the increase of stellar mass solely through mergers from z = 0.8 can make the massive galaxies a factor \sim 2 larger than observed at z = 0 , unless the satellite stellar mass is scattered to intra-cluster stars by gravitational tidal stripping or to the extended halo around the central galaxy that is not counted in the local observation .
We can also predict stellar mass functions of redshifts up to z \sim 3 , and the results are consistent with the latest observations .
Future more precise observational data will allow us to better constrain our model .