Linking the Langevin equation to scaling properties of space plasma turbulence at sub-ion scales

Current understanding of the kinetic-scale turbulence in weakly collisional plasmas still remains elusive. We employ a general framework in which the turbulent energy transfer is envisioned as a scale-to-scale Langevin process. Fluctuations in the sub-ion range show a global scale invariance, thus suggesting a homogeneous energy repartition. In this Letter, we interpret such a feature by linking the drift term of the Langevin equation to scaling properties of fluctuations. Theoretical expectations are verified on solar wind observations and numerical simulations, thus giving relevance to the proposed framework for understanding kinetic-scale turbulence in space plasmas.