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

Let X[rho] be a jump Lévy process of intensity [rho] which is close to the Wiener process if [rho] is big. We study the behavior of shifted small ball probability, namely, P{supt[set membership, variant][0,1]X[rho](t)-[lambda]f(t)[less-than-or-equals, slant]r} under all possible relations between the parameters r-->0, [rho]-->[infinity], [lambda]-->[infinity]. The shift function f is of bounded variation of its derivative.