The problem of propagation of a high-intensity light beam in a half-space with random inhomogeneities is treated. An exact solution is constructed through a functional integral representation. For a Gaussian random field, the exact moments of solution are given explicitly. A functional phase-integral method is developed to provide an asymptotic evaluation of the moment integrals. The method is applied to two problems in a stochastic laser beam propagation in random media with a homogeneous background or with a focusing effect.