The path integral representation of stochastic dynamics is equivalent to the traditional understanding of SDEs as of a continuous time limit of stochastic difference equations where different choices of parameter α α are called "interpretations" of SDEs. The choice α α = 1 / 2 , for which F 1 / 2 = F and which is known in quantum theory as Weyl symmetrization rule, is known as the Stratonovich interpretation, whereas α α = 1 as the Ito interpretation. While in quantum theory the Weyl symmetrization is preferred because it guarantees hermiticity of Hamiltonians, in STS the Stratonovich–Weyl approach is preferred because it corresponds to the most natural mathematical meaning of the finite-time SEO discussed below —the stochastically averaged pullback induced by the SDE-defined diffeomorphisms.