  Bi-Directional Grid Constrained (BGC) stochastic processes (BGCSP) are
constrained It\^{o} diffusions with the property that the further they drift
away from the origin, the more resistance to movement in that direction they
undergo. We investigate the underlying characteristics of the BGC parameter
$\Psi (x, t)$ by examining its geometric properties. The most appropriate
convex form for $\Psi$, i.e. the parabolic cylinder is identified after
extensive simulation of various possible forms. The formula for the resulting
hidden reflective barrier(s) is determined by comparing it with the simpler
Ornstein-Uhlenbeck process (OUP). Applications of BGCSP arise when a series of
semipermeable barriers are present, such as regulating interest rates and
chemical reactions under concentration gradients, which gives rise to two
hidden reflective barriers.
