Large deviation principle for stochastic slow–fast system with nonlinear multiplicative fractional Brownian motion

This paper focuses on a class of stochastic slow–fast differential equations driven by Brownian motion and fractional Brownian motion with Hurst parameter [Formula: see text]. First, we introduce a decomposition for the increment of fractional Brownian motion on [Formula: see text] and establish [Formula: see text]-estimations for the associated mixed Wiener–Young integral. Second, using the stochastic sewing lemma, we derive [Formula: see text]-estimations for the controlled system. Finally, we establish a large deviation principle for the slow component via the weak convergence method, viable pair method and averaging principle.