  We derive a novel framework called Bi-Directional Grid Constrained (BGC)
stochastic processes in which the further an Ito diffusion drifts away from the
origin, then the further it will be constrained. By making suitable
modifications to the Law of Iterated Logarithm (LIL), we derive a novel theorem
about the upper and lower bounds for BGC processes and their hidden barrier. To
visualize the theorem, we run many simulations of the Ito diffusions for a
representative expression for lambda(X, t), both before and after BGC and
uncover some interesting results with applications into finance and many other
areas.
