  The excursion set theory based on spherical or ellipsoidal gravitational
collapse provides an elegant analytic framework for calculating the mass
function and the large-scale bias of dark matter haloes. This theory assumes
that the perturbed density field evolves stochastically with the smoothing
scale and exhibits Markovian random walks in the presence of a density barrier.
Here we derive an analytic expression for the halo bias in a new theoretical
model that incorporates non-Markovian extension of the excursion set theory
with a stochastic barrier. This model allows us to handle non-Markovian random
walks and to calculate perturbativly these corrections to the standard
Markovian predictions for the halo mass function and halo bias. Our model
contains only two parameters: kappa, which parameterizes the degree of
non-Markovianity and whose exact value depends on the shape of the filter
function used to smooth the density field, and a, which parameterizes the
degree of stochasticity of the barrier. Appropriate choices of kappa and a in
our new model can lead to a closer match to both the halo mass function and
halo bias in the latest N-body simulations than the standard excursion set
theory.
