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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:
60G46Martingales and classical analysis
60H07Stochastic calculus of variations and the Malliavin calculus
60G44Martingales with continuous parameter
60H05Stochastic integrals