Moderate Deviations Type Evaluation for Integral Functionals of Diffusion Processes
R. Liptser, Vladimir Grigor'evich Spokoiny · Electronic Journal of Probability · 1999
We establish a large deviations type evaluation for the family of integral functionalswhere Ψ and g are smooth functions, ξ ε t is a "fast" ergodic diffusion while X ε t 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 t 0 g(ξ ε s )ds) t≥0 , ε 0 which has an independent interest as well.In addition, we give a preview for a vector case.