On the contribution of multiplicative noise terms to the Langevin equation for rotational relaxation

The Langevin equation for the rotational Brownian motion of two and three dimensional rotators has multiplicative noise terms if it is transformed into an equation for the dipole moment. It has been heuristically argued following Langevin that the average of the multiplicative noise terms vanishes for the inertial response. This enables one to write down the hierarchy of differential-difference equations governing the time behavior of the averages of the solution (usually generated by separating the variables in the Fokker–Planck equation) directly from the transformed Langevin equation. It is shown by interpreting the transformed Langevin equation as a Stratonovich equation how the assumption that the average of the multiplicative noise terms vanishes is justified.