Discrete-time inference for slow-fast systems driven by fractional Brownian motion

S Bourguin, S Gailus, K Spiliopoulos - Multiscale Modeling & Simulation, 2021 - SIAM
Multiscale Modeling & Simulation, 2021SIAM
We study statistical inference for small-noise-perturbed multiscale dynamical systems where
the slow motion is driven by fractional Brownian motion. We develop statistical estimators for
both the Hurst index as well as a vector of unknown parameters in the model based on a
single time series of observations from the slow process only. We prove that these
estimators are both consistent and asymptotically normal as the amplitude of the
perturbation and the time-scale separation parameter go to zero. Numerical simulations …
We study statistical inference for small-noise-perturbed multiscale dynamical systems where the slow motion is driven by fractional Brownian motion. We develop statistical estimators for both the Hurst index as well as a vector of unknown parameters in the model based on a single time series of observations from the slow process only. We prove that these estimators are both consistent and asymptotically normal as the amplitude of the perturbation and the time-scale separation parameter go to zero. Numerical simulations illustrate the theoretical results.
Society for Industrial and Applied Mathematics
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