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@article{Gehringer:2022:1361-6544/ac4818,
author = {Gehringer, J and Li, X-M and Sieber, J},
doi = {1361-6544/ac4818},
journal = {Nonlinearity},
pages = {1--37},
title = {Functional limit theorems for volterra processes and applications to homogenization},
url = {http://dx.doi.org/10.1088/1361-6544/ac4818},
volume = {35},
year = {2022}
}

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TY  - JOUR
AB  - 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 ε→0 of the solution of the random ordinary differential equation (ODE) ddtxεt=1ε√f(xεt,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 the random ODE converge to those of the Kunita type Itô SDE dxt=G(xt,dt), where G(x,t) is a semi-martingale with spatial parameters.
AU  - Gehringer,J
AU  - Li,X-M
AU  - Sieber,J
DO  - 1361-6544/ac4818
EP  - 37
PY  - 2022///
SN  - 0951-7715
SP  - 1
TI  - Functional limit theorems for volterra processes and applications to homogenization
T2  - Nonlinearity
UR  - http://dx.doi.org/10.1088/1361-6544/ac4818
UR  - http://iopscience.iop.org/article/10.1088/1361-6544/ac4818/meta
UR  - http://hdl.handle.net/10044/1/94071
VL  - 35
ER  -

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Professor Xue-Mei Li

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