The decay of excited nuclear systems is studied within the framework of the fluctuation-dissipation dynamics using the Langevin equations. The probability current through the barrier and the scission point are calculated for various ratios of the barrier height B(f) and the temperature T. The effect of the value of the viscosity and the type of initial conditions on the time evolution of this current is studied. Special attention is paid to the case B(f) = 0. A systematic comparison is made with the Kramers formula, which shows that it works surprisingly well in most cases, even when B(f)/T < 1. For the case B(f) = 0 the probability current calculated through the scission point is 1.5-2 times larger than the value obtained using the Kramers formula.