We establish a large deviations type evaluation for the family of integral functionals ε-κ √Tε0 Ψ (Xεs)g (ξεs) ds, ε ↘ 0, where Ψ and g are smooth functions, ξεt is a "fast" ergodic diffusion while Xεt is a "slow" diffusion type process, κ ∈ (0, 1/2). Under the assumption that g has zero barycenter with respect to the invariant distribution of the fast diffusion, we derive the main result from the moderate deviation principle for the family ε-κ √Tε0 Ψ (Xεs)g (ξεs) ds, ε ↘ 0 which has an independent interest as well. In addition, we give a preview for a vector case.
- Large deviations
- Moderate deviations