  L\'evy stochastic processes, with noise distributed according to a L\'evy
stable distribution, are ubiquitous in science. Focusing on the case of a
particle trapped in an external harmonic potential, we address the problem of
finding "shortcuts to adiabaticity": after the system is prepared in a given
initial stationary state, we search for time-dependent protocols for the
driving external potential, such that a given final state is reached in a
given, finite time. These techniques, usually used for stochastic processes
with additive Gaussian noise, are typically based on a inverse-engineering
approach. We generalise the approach to the wider class of L\'evy stochastic
processes, both in the overdamped and in the underdamped regime, by finding
exact equations for the relevant characteristic functions in Fourier space.
