The results of a series of particle‐in‐cell simulations of stochastic wave–particle interaction are presented. The threshold for stochasticity was confirmed. The simulations demonstrate that in a strong magnetic field plasma waves with quiver velocities much less than the speed of light but above a certain threshold can stochastically accelerate electrons to energies far greater than 1 MeV. Moreover, self‐consistency effects drive return currents and produce energetic runaway electrons that violate an invariant of motion.