[en] A statistical model for the bifurcation of the radial electric field E_r is analyzed in view of describing L-H transitions of toroidal plasmas. Noise in micro fluctuations is shown to lead to random changes of E_r, if a deterministic approach allows for more than one solution. The probability density function for and the ensemble average of E_r are obtained. The L-to-H and the H-to-L transition probabilities are calculated, and the effective phase limit is derived. Due to the suppression of turbulence by shear in E_r, the limit deviates from Maxwell's rule. (author)