  The excursion set model provides a convenient theoretical framework to derive
dark matter halo abundances. This paper generalizes the model by introducing a
more realistic merging and collapse process. A new parameter regulates the
influence of the environment and thus the coherence (non-Markovianity) of the
merging and the collapse of individual mass shells. The model mass function
also includes the effects of an ellipsoidal collapse. Analytic approximations
of the halo mass function are derived for scale-invariant power spectra with
the slopes $n=0,-1,-2$. The $n=-2$ mass function can be compared with the
results obtained from the `Hubble volume' simulations. A significant detection
of non-Markovian effects is found for an assumed accuracy of the simulated mass
function of 10%.
