Abstract
The analysis of a wide class of physical problems involves linear random differential equations—linear differential equations with stochastic coefficients. Here we consider the determination of probability densities for the solution processes of a class of linear random differential equations.This class is characterized by the property that the stochastic coefficients can be modeled by random processes with finite degrees of randomness. The solutions are examined by means of a Liouville-type equation satisfied by their joint probability densities. This technique is then applied to the study of electromagnetic fields in an inhomogeneous medium with special profiles.
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