Functional limit theorems for Volterra processes and applications to homogenization*
Functional limit theorems for Volterra processes and applications to homogenization*
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Volterra 过程的功能极限定理及其在均质化中的应用*
DOI：
10.1088/1361-6544/ac4818
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发表时间：
2022
期刊：
影响因子：
1.7
通讯作者：
Gehringer J
中科院分区：
文献类型：
--
作者：
Gehringer J
在粗路拓扑中证明了多维沃尔泰拉过程可加泛函的一个增强极限定理.作为应用，我们建立了随机常微分方程（ODE）解的弱收敛性，并证明了其极限解为高斯场驱动的粗糙微分方程，其漂移来自于极限粗糙驱动的L 'evy面积修正.进一步证明了随机常微分方程的随机流收敛于Kunita型Ito型It
We prove an enhanced limit theorem for additive functionals of a multi-dimensional Volterra processin the rough path topology. As an application, we establish weak convergence asof the solution of the random ordinary differential equation (ODE)and show that its limit solves a rough differential equation driven by a Gaussian field with a drift coming from the L\'evy 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 It\^o SDE, whereis a semi-martingale with spatial parameters.