Elliptic equations of higher stochastic order
Sergey V. Lototsky, Boris L. Rozovskii, Xiaoliang Wan (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
Similarity:
This paper discusses analytical and numerical issues related to elliptic equations with random coefficients which are generally nonlinear functions of white noise. Singularity issues are avoided by using the Itô-Skorohod calculus to interpret the interactions between the coefficients and the solution. The solution is constructed by means of the Wiener Chaos (Cameron-Martin) expansions. The existence and uniqueness of the solutions are established under rather weak assumptions, the main...