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Functional limit theorems for power series with rapid decay of moving averages of Hermite processes
Stochastics and Dynamics  (IF0.98),  Pub Date : 2021-03-03, DOI: 10.1142/s021949372150043x
Johann Rudolf Gehringer

We aim to obtain a homogenization theorem for a passive tracer interacting with a fractional, possibly non-Gaussian, noise. To do so, we analyze limit theorems for normalized functionals of Hermite–Volterra processes and extend existing results to cover 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 homogenization result for a slow/fast system driven by such Hermite noises.