A Fokker‐Planck (F‐P) formulation is used to describe electron avalanche breakdown in a high‐frequency field. It is shown that the dispersion term dominates the ``average electron'' term. The effect of the statistical fluctuations is to reduce the breakdown field and increase the rate of buildup of the electron population compared to the average electron theory. The F‐P coefficients, which are derived for an energy‐dependent collision frequency with an arbitrary ratio of laser frequency to collision frequency, are also useful for obtaining energy distributions in the theory of gaseous discharges. Numerical results are obtained for the e‐folding time in sapphire based on coefficients which were previously given by Zverevet al.in the context of average electron theory.