An example of large deviations for a stationary process

We give an example of large deviations for a family $(X_t^\varepsilon)_{t\ge 0}$, $\varepsilon >0$, with $\dot{X}_t^\varepsilon=a(X_t^\varepsilon)+b(X_t^\varepsilon) \eta_{t/\varepsilon}$, where $\eta_t$ is a stationary process obeying the Wold decomposition: $\eta_t=\int_{-\infty}^th(t-s)\,dN_s$ with respect to a homogeneous process $N_t$ with independent square integrable increments.