Stochastic PDEs
Abstract
In this chapter we revise some well-known tools for SPDEs. In the first section we collect methods from infinite dimensional stochastic analysis, in particular stochastic integration in Hilbert spaces. After this, we give an introduction to the variational approach to SPDEs by considering the stochastic heat equation. Finally, we present the theorems of Prokhorov and Skorokhod which are essential for the stochastic compactness method.
Keywords
Infinite dimensional stochastic analysis; Stochastic PDEs; Stochastic heat equation; Variational approach; Galerkin method; Compactness; Skorokhod's Theorem
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