Abstract
A Hilbert space-valued stochastic integration is defined for an integrator that is a cylindrical fractional Brownian motion in a Hilbert space and an operator-valued integrand. Since the integrator is not a semimartingale for the fractional Brownian motions that are considered, a different definition of integration is required. Both deterministic and stochastic operator-valued integrands are used. The approach uses some ideas from Malliavin calculus. In addition to the definition of stochastic integration, an Itô formula is given for smooth functions of some processes that are obtained by the stochastic integration.
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