Small ball probabilities for jump Lévy processes from the Wiener domain of attraction

Let Xρ be a jump Lévy process of intensity ρ which is close to the Wiener process if ρ is big. We study the behavior of shifted small ball probability, namely, P{supt∈[0,1]|Xρ(t)-λf(t)|⩽r} under all possible relations between the parameters r→0, ρ→∞, λ→∞. The shift function f is of bounded variation of its derivative.