分数阶噪声场中的扩散粗糙均匀化
Diffusive and rough homogenisation in fractional noise field
摘要：
最近开发的工具，我们证明了一个随机常微分方程的均匀化定理与短期和长期的依赖分数噪声。有效的动力学不一定是扩散，它们是由来自高斯和非高斯自相似普适类的随机过程同时驱动的随机微分方程给出的。一个关键的引理，这是'解除'联合功能中心和非中心极限定理在粗糙的路径拓扑。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
