论文标题
移动赫米特工艺的运动平均值的功能极限定理和均化的应用
Functional Limit Theorems of moving averages of Hermite processes and an application to homogenization
论文作者
论文摘要
我们的目的是在\ cite {gehringer-li标记的}中概括均质定理，以与分数gaußian噪声相互作用，以涵盖分数的非gaußian噪音。为此，我们分析了Hermite-Volterra过程的归一化函数的定理，将结果扩展在\ cite {diu-tran}到具有快速衰减系数的功率序列中。在远程依赖的情况下，我们在短期依赖性情况下或赫尔米特过程中获得了与维纳过程的收敛性。此外，我们证明了在多元案例中的收敛，而依赖性组件则是短期和远程依赖的组件。应用此定理，我们获得了由这种赫米特噪声驱动的缓慢/快速系统的均质结果。
We aim to generalize the homogenisation theorem in \cite{Gehringer-Li-tagged} for a passive tracer interacting with a fractional Gaußian noise to also cover fractional non-Gaußian noises. To do so we analyse limit theorems for normalized functionals of Hermite-Volterra processes, extending the result in \cite{Diu-Tran} to power series with fast decaying coefficients. We obtain either convergence to a Wiener process, in the short-range dependent case, or to a Hermite process, in the long-range dependent case. Furthermore, we prove convergence in the multivariate case with both, short and long-range dependent components. Applying this theorem we obtain a homogenisation result for a slow/fast system driven by such Hermite noises.
