  Presently, it is well established that fission of excited nuclei is a
dynamical process being a subject of fluctuations and dissipation. In the
literature, there are indications that, at the compact nucleus shapes, the
strength of nuclear friction is significantly reduced in comparison with the
prediction of the one-body approach. Thus, one can expect that at small
deformations the nuclear fission process occurs in the so-called "energy
diffusion regime". The purpose of our present work is to compare an approximate
analytical formula for the fission rate in this regime with the quasistationary
numerical rate which is exact within the statistical errors. Our calculations
demonstrate relatively good agreement between these two rates provided the
friction parameter is deformation independent. If one accounts for its
deformation dependence, the agreement becomes significantly poorer.
