Hidden Geometry of Bidirectional Grid-Constrained Stochastic Processes

Figure 11

Parabolic cylinder expression of for three different values of for and . Orange: inner-most barriers; green: middle barriers; purple: outer-most barriers. 10,000 BGC Itô diffusions simulated for various values of in . The general formula for a hidden reflective BGC barrier for a parabolic cylinder is further validated as and , where and for orange, for green, and for purple. Note that, for , for orange, for green, and for purple.