Abstract
There exists a satisfactory limit theory for stochastic integrals driven by finite dimensional semimartingales. The paper is an attempt to construct a corresponding theory in the case of processes with values in infinite dimensional Hilbert spaces. Limit theorems are given for scalar-and tensor-product integrals and for Hilbert-Schmidt integrands. As a corollary, a criterion for convergence or the tensor quadratic variation is established.
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