Taranto, Aldo 
ORCID: https://orcid.org/0000-0001-6763-4997 and Khan, Shahjahan ORCID: https://orcid.org/0000-0002-0446-086X and Addie, Ron ORCID: https://orcid.org/0000-0002-6664-8462
(2021)
Iterated logarithm bounds of bi-directional grid constrained stochastic processes.
Global and Stochastic Analysis, 8 (3).
pp. 19-39.
Abstract
We derive a novel framework called Bi-Directional Grid Constrained (BGC) stochastic processes in which the further an Itô 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 Itô diffusions for a representative expression for λ(X, t), both before and after BGC and uncover some interesting results with applications into finance and many other areas.
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