A comment on the Shibata–Hashitsume Langevin equation: Is it of the Stratonovich type or of the Ito type?

The Langevin equation derived by Shibata and Hashitsume with the help of the projection operator formula is shown to be the stochastic differential equation of the Ito type. From their derivation, it is natural to interpret it as that of the Stratonovich type. However, comparing the Shibata–Hashitsume (S–H) Langevin equation with the Langevin equation constructed within the framework of non-equilibrium thermo field dynamics (NETFD), the S–H Langevin equation seems to be that of the Ito type. By investigating this contradiction, it is found that the S–H Langevin equation leads to the consistent calculation when it is regarded as the stochastic equation of the Ito type.