  We analyze the full statistics of a stochastic squeeze process. The model's
two parameters are the bare stretching rate~$w$, and the angular diffusion
coefficient~$D$. We carry out an exact analysis to determine the drift and the
diffusion coefficient of $\log(r)$, where $r$ is the radial coordinate. The
results go beyond the heuristic lognormal description that is implied by the
central limit theorem. Contrary to the common "Quantum Zeno" approximation, the
radial diffusion is not simply $D_r = (1/8)w^2/D$, but has a non-monotonic
dependence on $w/D$. Furthermore, the calculation of the radial moments is
dominated by the far non-Gaussian tails of the $\log(r)$ distribution.
