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

Solesne Bourguin; Siragan Gailus; Konstantinos Spiliopoulos

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arXiv · 2007.11665

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

Solesne Bourguin·Siragan Gailus·Konstantinos Spiliopoulos

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Abstract

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.

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Solesne Bourguin, Siragan Gailus, Konstantinos Spiliopoulos. 2020-07-22. Discrete-time inference for slow-fast systems driven by fractional Brownian motion. https://arxiv.org/abs/2007.11665

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