On a class of semilinear stochastic systems in mechanics with quadratic-type nonlinearities: Time evolution of the probability density

AbstractThis paper supplies a mathematical analysis for a large class of stochastic systems described by ordinary differential equation of a semilinear type, with random initial conditions and parameters. The analysis of the abstract problem is realized in the first part of the paper with the objective of defining the existence and uniqueness conditions for the solution of the initial value problem. Then the quantitative analysis is realized on the basis of Adomian's decomposition method