  We show that in a hierarchical clustering model the low-order statistics of
the density and the peculiar velocity fields can all be modelled
semianalytically for a given cosmology and an initial density perturbation
power spectrum $P(k)$. We present such models for the two-point correlation
function $\xi(r)$, the amplitude $Q$ of the three-point correlation function,
the mean pairwise peculiar velocity $< v_{12}(r)> $, the pairwise peculiar
velocity dispersion $< v_{12}^2(r)>$, and the one-point peculiar velocity
dispersion $< v_1^2 >$. We test our models against results derived from N-body
simulations. These models allow us to understand in detail how these statistics
depend on $P(k)$ and cosmological parameters. They can also help to interpret,
and maybe correct for, sampling effects when these statistics are estimated
from observations. The dependence of the small-scale pairwise peculiar velocity
dispersion on rich clusters in the sample, for instance, can be studied
quantitatively. There are also significant implications for the reconstruction
of the cosmic density field from measurements in redshift space.
