  We use path integrals in order to estimate merger rates of dark matter haloes
using the Extended Press-Schechter approximation (EPS) for the Spherical
Collapse (SC) and the Ellipsoidal Collapse (EC) models. Merger rates have been
calculated for masses in the range $10^{10}M_{\odot}\mathrm{h}^{-1}$ to
$10^{14}M_{\odot}\mathrm{h}^{-1}$ and for redshifts $z$ in the range 0 to 3. A
detailed comparison between these models is presented. Path approach gives a
better agreement with the exact solutions for constrained distributions than
the approach of \cite{shto02}. Although this improvement seems not to be very
large, our results show that the path approach is a step to the right
direction. Differences between the two widely used barriers, spherical and
ellipsoidal, depend crucially on the mass of the descendant halo. These
differences become larger for decreasing mass of the descendant halo. The use
of additional terms in the expansion used in the path approach, other
improvements as well as detailed comparisons with the predictions of N-body
simulations, that could improve our understanding about the important issue of
structure formation, are under study.
