The current paper addresses white noise in dispersive optical solitons that is governed by the Schrödinger–Hirota equation with parabolic law of nonlinearity. Additional dispersive effects come from the spatio–temporal dispersion and the fourth–order dispersion that are included. The sub–ordinary differential equation method is implemented to retrieve the soliton solutions along with cnoidal waves and their type. The effect of white noise stays confined to the phase of the determined solitons and cnoidal waves.