A novel statistical technique which allows the asymptotic evaluation of second_ and higher_order averaged observables related to the stochastic complex parabolic equation is applied to the problem of beam propagation in a focusing medium characterized by random_axis misalignments. Analytical and numerical results concerning on_ and off_axis statistics (e.g., the variance of intensity fluctuations, modal power transfer, the probability distribution density of the log_irradiance, etc.) are presented, and comparisons are made with previously reported findings.