The paper studies the effect of a weak periodic driving on metastable Wanni
er-Stark states. The decay rate of the ground Wannier-Stark states as a con
tinuous function of the driving frequency is calculated numerically. The th
eoretical results are compared with the experimental data of Wilkinson et n
l. [Phys. Rev. Lett. 76, 4512 (1996)] obtained for cold sodium atoms in an
accelerated optical lattice.