  In this paper, we consider the problem of statistical inference for
generalized Ornstein-Uhlenbeck processes of the type \[ X_{t} = e^{-\xi_{t}}
\left( X_{0} + \int_{0}^{t} e^{\xi_{u-}} d u \right), \] where \(\xi_s\) is a
L{\'e}vy process. Our primal goal is to estimate the characteristics of the
L\'evy process \(\xi\) from the low-frequency observations of the process
\(X\). We present a novel approach towards estimating the L{\'e}vy triplet of
\(\xi,\) which is based on the Mellin transform technique. It is shown that the
resulting estimates attain optimal minimax convergence rates. The suggested
algorithms are illustrated by numerical simulations.

Methodology;Probability