  We present the Bogoliubov's causal perturbative QFT, which includes only one
refinement: the creation-annihilation operators at a point, \emph{i.e.} for a
specific momentum, are mathematically interpreted as the Hida operators from
the white noise analysis. We leave the rest of the theory completely unchanged.
This allows avoiding infrared -- and ultraviolet -- divergences in the
transition to the adiabatic limit for interacting fields. Here we present the
inductive step. We are especially concentrated with the analysis of the second
order contribution to the scattering operator, and give explicit computations
using the calculus of integral kernel operators, \emph{i.e} contractions of
their vector-valued kernels, and splittings of the contractions into advanced
and retarded parts. Explicit example of QED is provided, together with the
detailed analysis of the key point in avoiding UV divergence.
