Maximum Entropy Analytical Solution for Stochastic Differential Equations Based on the Wiener-Askey Polynomial Chaos

Many measurements models are formalized in terms of a stochastic process relating its solution to some given observables. The expression of the measurement uncertainty for the solution requires the determination of its (joint) pdf evaluated in an assigned time window. Recently, polynomial chaos (PC) theory has been widely recognized as a promising technique in order to address the problem. However, the uncertainty estimation via PC requires the use of a Monte Carlo integration sampling strategy, which is notoriously computationally intensive. In this paper a novel approach was presented in order to achieve the PC uncertainty estimation on the basis of a purely analytical methodology, requiring only an optimization calculus