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Averaging principle for slow-fast fractional stochastic differential equations
Charles-Edouard Br\'ehier, Ibrahima Faye
https://arxiv.org/abs/2510.04129 https://

Averaging principle for slow-fast fractional stochastic differential equations
We prove the averaging principle for a class of stochastic systems. The slow component is solution to a fractional differential equation, which is coupled with a fast component considered as solution to an ergodic stochastic differential equation driven by a standard Brownian motion. We establish the convergence of the slow component when the time-scale separation vanishes to the solution of the so-called averaged equation, which is an autonomous fractional differential equation, in the mean-sq…