  Parametric integration with hyperlogarithms so far has been successfully used
in problems of high energy physics (HEP) and critical statics. In this work,
for the first time, it is applied to a problem of critical dynamics, namely, a
stochastic model of developed turbulence in high-dimensional spaces, which has
a propagator that is non-standard with respect to the HEP: $(-i \omega + \nu
k^2)^{-1}$. Adaptation of the hyperlogarithm method is carried out by choosing
a proper renormalization scheme and considering an effective dimension of the
space. Analytical calculation of the renormalization group functions is
performed up to the fourth order of the perturbation theory,
$\varepsilon$-expansion of the critical exponent $\omega$ responsible for the
infrared stability of the fixed point is obtained.
