论文标题
分数噪声场的扩散和粗糙的均质化
Diffusive and rough homogenisation in fractional noise field
论文作者
论文摘要
借助最近开发的工具，我们证明了具有短且依赖性分数噪声的随机选的均质定理。有效的动力学不一定是扩散，它们是由由高斯和非高斯和非高斯自相似性普遍性类别的随机过程同时驱动的随机微分方程给出的。为此，关键的引理是在粗糙路径拓扑中的“抬高”关节功能中心和非中央极限定理。
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 given by stochastic differential equations driven simultaneously by stochastic processes from both the Gaussian and the non-Gaussian self-similarity universality classes. A key lemma for this is the `lifted' joint functional central and non-central limit theorem in the rough path topology.
