Functional Limit Theorems of moving averages of Hermite processes and an application to homogenization

2020/08/06 by Johann Gehringer, Gehringer, Johann
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Mathematical Dynamics and Fractals #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2008.02876

openalex publication_date 2020/08/06 · openalex created_date 2020/08/13 · openalex updated_date 2026/07/28

Abstract

We aim to generalize the homogenisation theorem in \citeGehringer-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 \citeDiu-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.

Citations

• Fractional Brownian Motions, Fractional Noises and Applications

Related

• Limit theorems for integral functionals of Hermite-driven processes
• Functional Limit Theorems for the Fractional Ornstein–Uhlenbeck Process
• Lower bound for local oscillations of Hermite processes
• Contributions to the asymptotic study of Hermite driven processes
• Homogenization with fractional random fields