Fourier series (solid lines) and SDE (symbols) solution of the distribution function, f, for the shock setup with Gaussian diffusion (α = 2, left panel) and superdiffusion (α = 1.7, right panel). We took the parameters a = −1 (corresponding to an advection in positive x direction) and κ_α = 1, and f is given at times t₁ = 1, t₂ = 10, and t₃ = 100. The dashed green line indicates the time-asymptotic steady state solution for Gaussian diffusion (Eq. (8)).