  This work deals with first hitting time densities of Ito processes whose
local drift can be modeled in terms of a solution to Burgers equation. In
particular, we derive the densities of the first time that these processes
reach a moving boundary. We distinguish two cases: (a) the case in which the
process has unbounded state space before absorption, and (b) the case in which
the process has bounded state space before absorption. The reason as to why
this distinction has to be made will be clarified.
  Next, we classify processes whose local drift can be expressed as a linear
combination to solutions of Burgers equation. For example the local drift of a
Bessel process of order 5 can be modeled as the sum of two solutions to Burgers
equation and thus will be classified as of class $\mathcal{B}^2$.
Alternatively, the Bessel process of order 3 has a local drift that can be
modeled as a solution to Burgers equation and thus will be classified as of
class $\mathcal{B}^1$. Examples of diffusions within class $\mathcal{B}^1$, and
hence those to which the results described within apply, are: Brownian motion
with linear drfit, the 3D Bessel process, the 3D Bessel bridge, and the
Brownian bridge.
