Nonrecursive statistics for integral equation solutions

摘要

Recursive schemes are often used to solve complex governing equations in mathematical physics. It is demonstrated that such an approach poses unique difficulties when applied to stochastic integral equations. Each subsequent term in the series requires knowledge of higher order statistics than evaluated for the previous term, and thus no true recursion exists. In effect, even if the equation is linear, it is nonlinear in stochastic quantities. The complexity of each term prevents the evaluation of more than a few terms in the iteration, even when symbolic manipulation codes such as MACSYMA are used.