Figure 3. We generated two Ornstein-Uhlenbeck processes with the same parameter set except for different α and in turn, exhibits different Ollivier-Ricci curvatures:

κ(x, y) = 0.6321 (red) with α = 1.0 and κ(x, y) = 0.0952 with α = 0.1 For both signals, Ornstein-Uhlenbeck process parameters were initialized with x(0) = 1 with σ = 1. One can see that Δκ × Δα ≥ 0 for this broad set of stochastic processes.