Purpose: The aim of this study is to introduce the stochastic dispersive Schrödinger–Hirota equation with parabolic law nonlinearity (SHEPL) with multiplicative white noise via Ito calculus and investigate its stochastic optical soliton solutions. For this purpose, we used unified Riccati equation expansion (UREEM) and a sub-version of an auxiliary methods to construct analytical solutions. Methodology: Firstly, we implemented traveling wave transform into SHEPL with multiplicative white noise via Ito calculus and constructed imaginary and real parts of its nonlinear ordinary differential equation (NODE) form. Then, we presented solution algorithms of UREEM and a sub-version of an auxiliary methods and successfully implemented to obtained NODE. We created analytical solutions of SHEPL with using the appropriate solution sets which involve unknown parameters and necessary transformations. Then we presented graphical representations of these solution functions by investigating the noise effect on the soliton structure and presented the gained results. Findings: We proposed the stochastic SHEPL equation for the first time in this article. We obtained stochastic optical soliton solutions, reflected their graphical representations and also observed effect of noise factor on the obtained soliton structure. Originality: The stochastic model of SHEPL has not been studied and the results have not been reported.