2021/04/17 by David P. Herzog, Hung D. Nguyen, Herzog, David P. +1
Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Mathematics #Particle Dynamics in Fluid Flows #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2104.08629
openalex publication_date 2021/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a system of Skorokhod stochastic differential equations (SDEs) modeling the pairwise dispersion (in spatial dimension d=2) of heavy particles transported by a rough self-similar, turbulent flow with Hölder exponent h∈ (0,1). Under the assumption that h>0 is sufficiently small, we use Lyapunov methods and control theory to show that the Markovian system is nonexplosive and has a unique, exponentially attractive invariant probability measure. Furthermore, our Lyapunov construction is radially sharp and gives partial confirmation on a predicted asymptotic behavior with respect to the Hölder exponent h of the invariant probability measure. A physical interpretation of the asymptotics is that intermittent clustering is weakened when the carrier flow is sufficiently rough.