  A distributional equation as a criterion for invariant measures of Markov
processes associated to L\'evy-type operators is established. This is obtained
via a characterization of infinitesimally invariant measures of the associated
generators. Particular focus is put on the one-dimensional case where the
distributional equation becomes a Volterra-Fredholm integral equation, and on
solutions to L\'evy-driven stochastic differential equations. The results are
accompanied by various illustrative examples.
