Al-Hussein, Abdulrahman Martingale representation theorem in infinite dimensions. (English) Zbl 1058.60028 Arab J. Math. Sci. 10, No. 1, 1-18 (2004). Summary: We prove a martingale representation theorem for Hilbert space valued martingales, adapted to filtration generated by a given Wiener process \(W\) on another separable Hilbert space \(H\). Two cases are considered: first when \(W\) is cylindrical, and second when \(W\) is a genuine \(Q\)-Wiener process on \(H\). A Clark-Ocone theorem is derived in this setting to give an explicit form for the integrand in this theorem. Cited in 3 Documents MSC: 60G46 Martingales and classical analysis 60H07 Stochastic calculus of variations and the Malliavin calculus 60G44 Martingales with continuous parameter 60H05 Stochastic integrals Keywords:cylindrical Wiener process; Wiener space; martingale representation theorem; Clark-Ocone theorem PDFBibTeX XMLCite \textit{A. Al-Hussein}, Arab J. Math. Sci. 10, No. 1, 1--18 (2004; Zbl 1058.60028)