1. Certain ways of utilizing analogous methods in statistical hydrodynamics (in the theory of turbulence) were mentioned in reference [12].
2. In essence, the apparatus of functional integration appeared in the these works in solving differential equations in the infinite dimensional space of quantum field theory (the so-called “Schwinger equations” in variational derivatives).
3. If the functional F[x(τ)] = F[x(τ),τ] depends explicitly on τ, then F[X0+x(τ),t0+τ]must appear on the right side of this formula under the integral sign.
4. After the appropriate normalization the integral (1.28) expresses the mean value of the function F(u) where u = Σbjxj is a linear combination of random variables distributed according to a multidimensional normal law with a zero vector of mean values and a matrix of second moments equal to 12(ajk)−1; from this, it develops thatuis also normally distributed with a mean value 0 and a dispersion equal to c2∕2.
5. It is possible, of course, to raise the question of the numerical integration of integrals over Wiener measure; the first results in this direction are contained in work of Cameron [10a]. However, we will not concern ourselves with this question here.