# 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}
}
• Published 13 April 2021
• Mathematics
• Nonlinearity
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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## References

SHOWING 1-10 OF 89 REFERENCES
Functional limit theorems for power series with rapid decay of moving averages of Hermite processes
We aim to obtain a homogenization theorem for a passive tracer interacting with a fractional, possibly non-Gaussian, noise. To do so, we analyze limit theorems for normalized functionals of
Diffusive and rough homogenisation in fractional noise field
• Mathematics
• 2020
With recently developed tools, we prove a homogenisation theorem for a random ODE with short and long-range dependent fractional noise. The effective dynamics are not necessarily diffusions, they are
Deterministic homogenization under optimal moment assumptions for fast-slow systems. Part 1
• Mathematics
• 2020
We consider deterministic homogenization (convergence to a stochastic differential equation) for multiscale systems of the form \[ x_{k+1} = x_k + n^{-1} a_n(x_k,y_k) + n^{-1/2} b_n(x_k,y_k), \quad
Functional Limit Theorems for the Fractional Ornstein–Uhlenbeck Process
• Mathematics
Journal of Theoretical Probability
• 2020
We prove a functional limit theorem for vector-valued functionals of the fractional Ornstein–Uhlenbeck process, providing the foundation for the fluctuation theory of slow/fast systems driven by both