  It is believed that the biasing of the galaxies plays an important role for
understanding the large-scale structure of the universe. In general, the
biasing of galaxy formation could be stochastic. Furthermore, the future galaxy
survey might allow us to explore the time evolution of the galaxy distribution.
In this paper, the analytic study of the galaxy-mass density relation and its
time evolution is presented within the framework of the stochastic biasing. In
the weakly non-linear regime, we derive a general formula for the galaxy-mass
density relation as a conditional mean using the Edgeworth expansion. The
resulting expression contains the joint moments of the total mass and galaxy
distributions. Using the perturbation theory, we investigate the time evolution
of the joint moments and examine the influence of the initial stochasticity on
the galaxy-mass density relation. The analysis shows that the galaxy-mass
density relation could be well-approximated by the linear relation. Compared
with the skewness of the galaxy distribution, we find that the estimation of
the higher order moments using the conditional mean could be affected by the
stochasticity. Therefore, the galaxy-mass density relation as a conditional
mean should be used with a caution as a tool for estimating the skewness and
the kurtosis.
