A White Noise Approach to Stochastic Neumann Boundary-Value Problems

Abstract

We illustrate the use of white noise analysis in the solution of stochastic partial differential equations by explicitly solving the stochastic Neumann boundary-value problem

$$ LU(x) - c(x)U(x) = 0,x \in D \subset ^d $$

$$\gamma (x) \cdot \nabla U(x) = - W(x),x \in \partial D, $$

where L is a uniformly elliptic linear partial differential operator and W(x), x ∈ ℝ^d, is d-parameter white noise.