Solving linear stochastic differential equations

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Abstract
The aim of this paper is to provide the user with tools for the solution of linear differential equations with random coefficients. Only analytic methods which lead to expressions in closed form for first and second order moments and probability distributions of the solution are considered. The paper deals both with approximate methods which require the existence of a small (or large) dimensionless parameter and with the method of model coefficients, where the true coefficients of the stochastic equation are replaced by random step functions with the same first and second order moments and probability distributions, chosen in such a way that the equation can be solved analytically. The second procedure does not rely on the existence of a small parameter.