  Stochastic processes that are randomly reset to an initial condition serve as
a showcase to investigate non-equilibrium steady states. However, all existing
results have been restricted to the special case of memoryless resetting
protocols. Here, we obtain the general solution for the distribution of
processes in which waiting times between reset events are drawn from an
arbitrary distribution. This allows for the investigation of a broader class of
much more realistic processes. As an example, our results are applied to the
analysis of the efficiency of constrained random search processes.
