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∈D⊂R d,γ(x)⋅∇U(x)=−W(x), x∈∂D, where L is a uniformly elliptic linear partial differential operator and W(x), x∈R d, is d-parameter white noise.
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Holden, H., Øksendal, B. A White Noise Approach to Stochastic Neumann Boundary-Value Problems. Acta Applicandae Mathematicae 63, 141–150 (2000). https://doi.org/10.1023/A:1010730510108
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DOI: https://doi.org/10.1023/A:1010730510108