On \(L^ p\) stochastic representations
The author proves the following integral representation result for stochastic integrals: Let \(w\) be a Brownian motion on \((\Omega, F^w, P)\). Then \(f \in L_p (F_\infty, P)\), \(1 < p < \infty\), has a representation as \(f = E |f |+ \int^\infty_0 Hdw\), where \(H \in L_p (dw)\), \(L_p (dw) : = \{H \in \wp\mid |H |_\infty < \infty\}\), \(|H |_p = |\int^\infty_0(H^2ds)^{1/2} |_{L_p}\). The representation is unique.
stochastic \(p\)-integral representation
scientific article; zbMATH DE number 820287