t and having Lévy measure $\nu$ is asymptotically equivalent to estimating $f$ from the Gaussian white noise model  $$dy_t=\sqrt{f(t)}dt+\frac{0}{0\sqrt{T_n g(t)}}dW_t,\quad g=\frac{d\nu_0}{d{\ensuremath{\textnormal{Leb}}}},\quad t\in I.$$ 