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Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2022

Asymptotic preserving schemes for SDEs driven by fractional Brownian motion in the averaging regime

Résumé

We design numerical schemes for a class of slow-fast systems of stochastic differential equations, where the fast component is an Ornstein-Uhlenbeck process and the slow component is driven by a fractional Brownian motion with Hurst index H ą 1{2. We establish the asymptotic preserving property of the proposed scheme: when the timescale parameter goes to 0, a limiting scheme which is consistent with the averaged equation is obtained. With this numerical analysis point of view, we thus illustrate the recently proved averaging result for the considered SDE systems and the main differences with the standard Wiener case.
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Dates et versions

hal-03211906 , version 1 (29-04-2021)

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Charles-Edouard Bréhier. Asymptotic preserving schemes for SDEs driven by fractional Brownian motion in the averaging regime. Journal of Mathematical Analysis and Applications, 2022, 509 (1), pp.125940. ⟨10.1016/j.jmaa.2021.125940⟩. ⟨hal-03211906⟩
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