Embedding the abstract Wiener space in a probability space
Consider an abstract Wiener process \((W,w,H)\), embedded in a probability space \((\Omega,{\mathcal F},\mathbb{P})\), in the sense that \(w\) is a \(W\)-valued Gaussian variable, with \(H\) as reproducing space. On the one hand, a simple conditional Malliavin calculus is defined, by differentiating only in the direction of \(w\). On the other hand, an Itô integral is constructed, starting from an adapted continuous resolution of identity on \(H\). These two extensions are applied to a filtering problem, yielding dimension-free Girsanov-like formulas, and to a representation of martingale results.
scientific article; zbMATH DE number 1423455