  We analyse four approaches to elimination of a fast variable, which are
applicable to systems like passive Brownian particles: (i) moment formalism,
(ii) corresponding cumulant formalism, (iii) Hermite function basis, (iv)
formal `cumulants' for the Hermit function basis. The accuracy and its strong
order are assessed. The applicability and performance of two first approaches
are also demonstrated for active Brownian particles.
