A stochastic dynamic model for the induced rain attenuation on multiple radio links is presented in this paper. The model is considered as a generalization of the well-known and well-accepted Maseng–Bakken model in $n$-dimensions. It incorporates the spatial and time behavior of the rain attenuation phenomena and provides an analytical expression for the transition probability distribution. It consists of a system of stochastic differential equations (SDEs), which, except for the solid mathematical formulation of the correlated rain attenuation stochastic processes, constitutes the general framework for the calculation of other statistical quantities useful for the radio system designers. The long-term statistics and the dynamic properties of rain attenuation are used for the parameterization of the model, without the constraint of any built-in assumptions of the rain field. Finally, the proposed model is used for the generation of correlated rain attenuation time series on multiple satellite communication slant paths and especially to diversity schemes, including site and orbital (angle) diversity. The derived results from the model are tested with respect to experimental long-term statistics for various geometries with very encouraging results. The limitations and the ranges of applicability of the model for Earth–space diversity systems are reported, and the sensitivity of the model on the crucial parameters is discussed.