Large Deviation Principle for Stochastic Differential System Pertubated by a Rapid Process in the Besov-Orlicz Topology

In this study, we want to analyze a large deviation principle associated with a family processxε=(xεt),t≥0in the Besov-Orlicz space whose drift coefficient is additionally perturbed by a strictlystationary processζ= (ζt),t≥0, defined on the probability space(Ω,Fζ,(Fζt)t≥0,Pζt),withvalues in a general Polish spaceE. The processxεis a solution of Itô integral:xεt=x0+∫t0b(xεs,ζs/ε)ds+√ε∫t0σ(xεs)dwsx0=x∈Rdin which the conditionζis independent of the brownian motionwand obeys a large deviationprinciple with a rate functionIζ.