Abstract
A theory of Hilbert-space-valued traces and multiple integration is developed for kernels inL2([0, 1]p × Θ). The multiple Ogawa and the multiple Stratonovich integrals for such kernels are introduced and sufficient conditions for their existence are obtained. The derivation of the Hu-Meyer formula connecting the multiple Ogawa and the multiple Stratonovich integrals requires the introduction of traces of random kernels. Such a derivation is obtained under appropriate conditions.
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