  We use the Excursion Set formalism to compute the properties of the halo mass
distribution for a stochastic barrier model which encapsulates the main
features of the ellipsoidal collapse of dark matter halos. Non-markovian
corrections due to the sharp filtering of the linear density field in real
space are computed with the path-integral technique introduced by Maggiore &
Riotto (2010). Here, we provide a detailed derivation of the results presented
in Corasaniti & Achitouv (2011) and extend the mass function analysis to higher
redshift. We also derive an analytical expression for the linear halo bias. We
find the analytically derived mass function to be in remarkable agreement with
N-body simulation data from Tinker et al. (2008) with differences smaller than
~5% over the range of mass probed by the simulations. The excursion set
solution from Monte Carlo generated random walks shows the same level of
agreement, thus confirming the validity of the path-integral approach for the
barrier model considered here. Similarly the analysis of the linear halo bias
shows deviations no greater than 20%. Overall these results indicate that the
Excursion Set formalism in combination with a realistic modeling of the
conditions of halo collapse can provide an accurate description of the halo
mass distribution.
