Functional limit theorems for Volterra processes and applications to homogenization

@article{Gehringer2022FunctionalLT,
  title={Functional limit theorems for Volterra processes and applications to homogenization},
  author={Johann Gehringer and Xue-mei Li and Julian Sieber},
  journal={Nonlinearity},
  year={2022},
  volume={35},
  pages={1521 - 1557}
}
We prove an enhanced limit theorem for additive functionals of a multi-dimensional Volterra process (yt)t⩾0 in the rough path topology. As an application, we establish weak convergence as ɛ → 0 of the solution of the random ordinary differential equation (ODE) ddtxtε=1εf(xtε,ytε) and show that its limit solves a rough differential equation driven by a Gaussian field with a drift coming from the Lévy area correction of the limiting rough driver. Furthermore, we prove that the stochastic flows of… 
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