Abstract
This paper deals with the construction of mean square real-valued solutions to both initial and boundary value problems of linear differential equations whose coefficients are assumed to be stochastic processes and, initial and boundary conditions are random variables. A key result to conduct our study is the extension of the Leibniz integral rule to the random framework taking advantage of the so-called random Fourth Calculus. Exact expressions for the main statistical functions (average and variance) associated to the solutions to both problems are also provided. Illustrative examples computing the average and standard deviation are included.
