Stochastic versus deterministic

One of the fundamental problems in stochastic modeling of dynamic systems is to what extent the study of stochastic analysis differs with corresponding deterministic analysis. This work focuses the attention of finding estimates on the variation of stochastic solutions and the corresponding solution of the mean of the dynamic system. This is analyzed in the context of random polynomials and differential equations. Certain analytic and computational study is made with regard to random differential equations and algebraic polynomials.