In this work we analyse the stochastic dynamics of initially low-energy weakly relativistic particles moving under the action of electrostatic waves. The relevant phase space is not well described by standard nonlinear pendulum approximations, but appropriate resonance studies based on the overlap of primary and secondary islands show that three regions may be identified as the wave vector k of the electrostatic mode is varied: one for small values of k, where the dynamics is always relativistic and regular; one for moderately large values of k, where the dynamics is always relativistic, being regular for small field amplitudes and stochastic for large field amplitudes; and finally one for fairly large values of k, where the dynamics is relativistic and regular for small amplitudes of the wave field and non-relativistic and stochastic for larger values of the amplitude. We perform an extensive numerical analysis in order to check our analytical estimates, and finally we present a brief numerical study of particle diffusion in the relativistic stochastic regime.