2025/06/09 by Paolo Cifani, Cifani, Paolo, Franco Flandoli +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Fractional Differential Equations Solutions #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and financial applications #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2506.08068
openalex publication_date 2025/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Stochastic transport due to a velocity field modeled by the superposition of small-scale divergence free vector fields activated by Fractional Gaussian Noises (FGN) is numerically investigated. We present two non-trivial contributions: the first one is the definition of a model where different space-time structures can be compared on the same ground: this is achieved by imposing the same average kinetic energy to a standard Ornstein-Uhlenbeck approximation, then taking the limit to the idealized white noise structure. The second contribution, based on the previous one, is the discover that a mixing spatial structure with persistent FGN in the Fourier components induces a classical Brownian diffusion of passive particles, with suitable diffusion coefficient; namely, the memory of FGN is lost in the space complexity of the velocity field.