The Langevin equations for quasi-linear wave–particle interaction are obtained taking advantage of the unequivocal equivalence between the Fokker–Planck equation and the former ones. The Langevin equations are solved numerically and, hence, the evolution of a single particle embedded in an electromagnetic field in momentum space is obtained. The equations are relativistic and valid for any wave. It is also shown that the stochastic part of the equations is negligible in comparison with the deterministic term, except for the momentum close to the resonance condition for the main parallel refractive index.