Hidden Geometry of Bidirectional Grid-Constrained Stochastic Processes

Figure 4

Potential convex candidates for . Blue: without BGC; red: with BGC 10,000 unconstrained and 10,000 BGC Itô diffusions simulated. All the potential BGC functions are not suitable for the standard Itô diffusions of BGCSP, even though they are bidirectionally convex, except for (c). (a) and (c) were rejected, since they do not constrain to constant hidden barriers. (b) and (d) were rejected because whilst there is some initial evidence of constant hidden barriers, they become unstable over time and explode to , faster than unconstrained Itô diffusions. (a) . (b) . (c) . (d) .

(a)

(b)

(c)

(d)