Hidden Geometry of Bidirectional Grid-Constrained Stochastic Processes

Figure 9

BGC hidden reflective barriers relation to Ornstein-Uhlenbeck process. (a) Idealized BGC process: BGCSP involves Itô processes that start at an initial position , where the further they drift away from the long run mean , the slower they will approach the hidden barriers and , where and . (b) Idealized hybrid between BGCSP and OUP: via the reflection principle, we can better see the transition between the other two paradigms. (c) Idealized Ornstein-Uhlenbeck process: OUP involves Itô processes that can start at any initial position and will “gravitate” to the long-term mean .

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