  This work focuses on the slow-fast system perturbed by the mixed fractional
Brownian motion with Hurst parameter H\in(1/2,1). The integral with respect to
fractional Brownian motion is the generalized Riemann-Stieltjes integral and
the integral with respect to Brownian motion is standard Ito integral. We
establish large deviation principles with a good rate function for the slow
component. Our approach is based on the variational framework and the weak
convergence criteria for mixed fractional Brownian motion. By combining the
weak convergence method and Khasminskii's averaging principle, we show that the
controlled slow component weakly converges to a limit which is related to the
invariant measure of the uncontrolled fast component.

Probability