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Martingale representation theorem in infinite dimensions. (English) Zbl 1058.60028
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.
##### MSC:
 60G46 Martingales and classical analysis 60H07 Stochastic calculus of variations and the Malliavin calculus 60G44 Martingales with continuous parameter 60H05 Stochastic integrals